







The difference between two numbers is 3 
20180605 

From Hannah: write a pair if integers whose difference is 3 ( given that the greater number is 8 ) Answered by Penny Nom. 





Two odd integers 
20180604 

From Pleroma: The product of two alternate odd integers exceeds three times the smaller number by 12.
What is the larger number? Answered by Penny Nom. 





Three consecutive odd integers 
20171010 

From Johanna: Three consecutive odd integers are such that the sum of the first and second is 31 less than 3 times the third Answered by Penny Nom. 





Two consecutive odd integers 
20170714 

From Adeeb: Find two consecutive odd positive integers, sum of whose square is 290. Answered by Penny Nom. 





The smallest and largest 4 digit integers 
20170613 

From Avneetpal: Difference of the smallest and biggest 4digit number Answered by Penny Nom. 





Three consecutive natural numbers 
20170611 

From Anita: Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the square of the other two by 60. Find the numbers. Answered by Penny Nom. 





A puzzle with some integers 
20170330 

From Glen: Use 7,7,5,5 to equal 3 only using each # once and each math function once Answered by Penny Nom. 





Divisibility of 3n^5+7n 
20161214 

From Parag:
Question from Parag, a student:
if n is a natural number,then 3n^5+7n is divisible by
a)2
b)3
c)5
d)7
i got the answer but still i need a valid alternate approach. Answered by Penny Nom. 





The sum of three integers is 30 
20161206 

From Vaishnavi: _+_+_:30. Blanks are to be filled by(1,3,5,7,9,11,13,15) and numbers can be repeated. Answered by Penny Nom. 





Five consecutive even integers 
20160812 

From Marcelle: The average of 5 even consecutive numbers is 112. What is the largest numbers? Answered by Penny Nom. 





The difference between the ares of two rectangles 
20160609 

From Ingrid: I am trying to help my son with an area question.
I have the answer, from the solutions, but I cannot figure out how to teach him.
Question:
Two rectangles have lengths 13cm and 19cm respectively.
Their total area is 376cm squared.
If both their widths are whole numbers, what is the difference in their areas?
I know that this is solvable once I determine the widths of the rectangles ,
but how do I go about finding that?
Thanks for your help Answered by Chris Fisher and Harley Weston. 





Three consecutive integers 
20160107 

From ronn: Three consecutive integers whose sum is 186 Answered by Penny Nom. 





Four consecutive integers 
20160105 

From sherica: my teacher gave us an assignment and it says here that;
THERE ARE FOUR CONSECUTIVE INTEGERS.IF THE SMALLEST ONE IS x ,FIND THE SUM OF THE FOUR INTEGERS. that is the question ...thanks hope that u can answer it Answered by Penny Nom. 





Three consecutive integers 
20150328 

From Aleksey: I need help how do I find the second of three consecutive integers if the sum of the first and third is 26? Answered by Penny Nom. 





Two consecutive odd integers 
20150309 

From gowtham: The sum of two consecutive odd integers is 20.find the integers Answered by Penny Nom. 





Two consecutive positive integers 
20150301 

From meha: Find two consecutive positive integers , sum of whose squares is 365. Answered by Penny Nom. 





Even and odd 
20141128 

From Subrahmanya: n1, n2, n3....................,n1997 are integers not necessarily distinct. (actually in n1, n2,.............., n1997 the numbers 1,2,.................,1997 are subscripts of 'n')
X= (1)^n1+(1)^n2+............+(1)^n998
Y=(1)^n999+(1)^n1000+............+(1)^n1997
Then
which of the following options is true
A) (1)^X = 1, (1)^Y = 1 B) (1)^X = 1, (1)^Y = 1
C) (1)^X = 1, (1)^Y = 1 D) (1)^X = 1, (1)^Y = 1
E) none of these Answered by Penny Nom. 





Three consecutive odd integers 
20141017 

From Maddy: 3 times the largest of three consecutive odd integers is 13 more than the sum of the other two. What are the integers? Answered by Penny Nom. 





The largest odd number using the digits 08672 
20140624 

From audrey: what is a 5 digit greatest odd number out of this given digits? 08672 Answered by Robert Dawson. 





Consecutive Numbers Question 
20130811 

From Lucy: Hello,
I have a question about consecutive numbers. So lets say a question tells you to find what three consecutive numbers are that add up to a certain number. To calculate this, would you use
2x+1, 2x+3, 2x+5 or just x, x+2, x+4.
Also, the same question for even numbers. Would you use:
2x, 2x+2, 2x+4 or just x, x+2, x+4.
My math book is confusing because it uses the first strategy(the 2x+…) in some situations and the second strategy(x+…) in other situations. Thus, can you provide me an explanation of why you would use the strategy that is correct?
Specifically, my book answered this question: If “n” is the first of five consecutive odd numbers, what is their average, using n,n+2….=5n+20 and average is n+4(this is the answer),.
For the question: the sum of 4 consecutive odd integers must be:
Divisible by 8 but not necessarily 16(this is the answer), it used the strategy 2k+1, 2k+3…=8k+16.
Thank you so much for taking the time to answer my question. Answered by Harley Weston. 





Three consecutive odd integers 
20130708 

From sparsh: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is: Answered by Robert Dawson. 





If n is odd, then n^2  3 is even 
20121211 

From Tracy: Prove the statement:
For all integers n, if n is odd, then n2  3 is even. Answered by Penny Nom. 





Why is the letter Z used for the integers? 
20120611 

From ROSE: WHY is that the acronym of integers is represented by letter Z or J? Answered by Chris Fisher. 





Three consecutive odd integers 
20111007 

From Muneera: Find 3 consecutive odd integers so that 3 times their sum is 5 more than 8 times the middle one? Answered by Penny Nom. 





Three consecutive odd integers 
20101107 

From karen: find three consecutive odd integers such that twice the sum of the second and the third is 43 more that three times the first Answered by Penny Nom. 





A polynomial with integer coefficients 
20101023 

From Adori: Question from Adori, a student:
Find a polynomial with integer coefficients that has the given zeros: 2/3, 4, root of 3i, root of 3i. Answered by Harley Weston. 





Four consecutive integers 
20101021 

From Mickey: Find four consecutive integers such that the sum of the first three integers is 20 more then the fourth integer.
I know that for consecutive integers the algebraic expression is x+x+1+x+2+x+3 Answered by Penny Nom. 





The product of 2 consecutive integers 
20100628 

From Sharon: the product of 2 consecutive integers is 6 less than the square of the larger number.
find the smaller number Answered by Penny Nom. 





Odd integers 
20100528 

From jack: If x is an odd integer, which of the following must also be an odd integers
a) x+1; b) 2x; c) x+4; d) x1; e) x/2? Please help me to solve this problem. Thank you. Answered by Penny Nom. 





The product of two consecutive even integers 
20100511 

From Terry: The product of two consecutive even integers is 14 more than their sum. Find the integers. Answered by Penny Nom. 





7 odd numbers 
20100219 

From mike: Hello there,
Problem: find 7 odd numbers who sum is equal to 30.
Hint*My professor said it's possible to add 7 odd numbers and get 30 for an answer!
and he said we can use Negative and rational numbers but no decimal or fractions.
So is there anyway of solving this? Please get back to ASAP! thanks. Answered by Harley Weston and Tyler Wood. 





Consecutive even integers 
20100203 

From cassandra: find 2 consecutive even integers whose sum is 34
find 3 consecutive even integers such that 3 time the middle interger is 10 more than the greatest. Answered by Tyler Wood. 





1^3 + 2^3 + 3^3 +4^3 ... n^3 = ? 
20100129 

From ireimaima: Hi..
Can u please help me with this question..
I find that when i test eg: n=2 for n (n+1) /4,
it seems that it does not giving me the right answer of 1^3 + 2^3 = 9
but 3/2... i'm confuse..can u please help me..thanks so much
Prove that:
1^3 + 2^3 + 3^3 +4^3………………………………..n^3 = n (n+1) /4 Answered by Penny Nom. 





Is it a square? 
20100129 

From Manick: I have a question. how to find whether a given integer is a perfect square or not? Answered by Robert Dawson. 





The cube of an integer 
20100120 

From Shankar: Can the cube of an integer end with 1985 ones ? Answered by Robert Dawson. 





Consecutive odd intergers 
20100106 

From keyanna: list five consecutive odd integers, starting with 3 Answered by Robert Dawson. 





A number base that's not a positive integer 
20091211 

From Nick: Is it possible for a number to have a base that's not a positive integer?
Base 1 gives a result that's meaningless but possible. I have no concept of a base 0, a negative base, or a fractional base, never mind any other base. I think there isn't any base that's not a positive integer, but, knowing that math keeps jumping ahead and sometimes has inventions before anyone knows how to exploit them, I think I'd better ask.
Thank you.
Nick Answered by Robert Dawson and Claude Tardif. 





Consecutive odd integers 
20091109 

From Erin: I'm having trouble with consecutive integers. i know it goes n + n + 1 + n + 2
and so on, but if its odd then do the numbers change to odd ones? i don't know
the question is: the sum of four consecutive odd integers is 72. write an equation to model
this situation and find the values of the four integers Answered by Robert Dawson and Penny Nom. 





Four consecutive odd integers 
20091024 

From Tonya: the sum of four consecutive odd intergers 2008 what are the intergers Answered by Penny Nom. 





A fourdigit positive integer 
20090904 

From TRACEY: I AM A FOURDIGIT POSITIVE INTEGER SUCH THAT THE SUM OF MY DIGITS IS 18 AND MY DIGITS REVERSED ARE EXACTLY FOUR TIMES GREATER THAN MYSELF. WHAT NUMBER AM I? Answered by Robert Dawson. 





Integers and decimals in day to day life 
20090629 

From mitichie: can you tell use of integers and decimals in our day to day life. Answered by Penny Nom. 





Finding an Array to an Integer Linear Programming Problem 
20090512 

From Debbie: how to make an array for 3 box of juice for 25 students and 2 teacher. 1 pack of juices
hols 3boxes the answer is 9 packages but how do you make array for this Answered by Janice Cotcher. 





Three consecutive odd integers 
20090402 

From Brian: Find the greatest of three consecutive odd integers if the product of the second and third is 8 more than 13 times the first. Answered by Robert Dawson. 





Three consecutive odd integers 
20090311 

From Susan: Find three consecutive odd integers such that the sum of the first, twice the second, and three times the third is 70 Answered by Penny Nom. 





Evaluating numeric expressions 
20090210 

From Jennifer: 521(350)164(299) Answered by Penny Nom. 





The resulting number is the square of an integer 
20090130 

From Randy: A positive integer n is chosen. Then the product n ( n + 1 )
is computed and two digits are appended to the end of the product. The
resulting number is the square of an integer.
Show that it is always possible to complete the process above or give a
positive integer n for which the process cannot be completed. Answered by Chris Fisher and Claude Tardif. 





Sheep, goats, and hogs 
20090123 

From La: A man buys sheep, goats, and hogs, to the number of 100, for 100 crowns; the sheep cost him 1/2 a crown apiece; the goats cost him 11/3 crowns apiece; and the hogs cost him 31/2 crowns apiece. How many had he of each? Answered by Robert Dawson. 





For which integers a, b, c does a  b  c = a  (b  c)? 
20090113 

From Johanna: For which integers a, b, c does a  b  c = a  (b  c)? Answered by Penny Nom. 





Finding an Unknown Integer Given Quotients and Remainders 
20081205 

From Mark: What is the least positive integer meeting each of the following conditions?
Dividing by 7 gives a remainder of 4.
Dividing by 8 gives a remainder of 5.
Dividing by 9 gives a remainder of 6. Answered by Janice Cotcher. 





Three consecutive odd integers 
20081103 

From kim: Determine three consecutive odd integers such that twice the sum of the second and third is 29 less than 5 times the first. Answered by Penny Nom. 





Three consecutive integers 
20081007 

From pam: Find three consecutive integers such that the greatest increased by twice the least is 293. Answered by Penny Nom & Chris Fisher. 





Three consecutive positive integers 
20080720 

From AC: find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 4 times the third Answered by Penny Nom. 





Four Positive Integers 
20080720 

From william: let a, b, c and n be positive integers. If a+b+c=(19)(97) and a+n=bn=c/n, compute the value of a. Answered by Janice Cotcher. 





The square root of (18*n*34) 
20080701 

From Peter: What is the least possible positive integervalue of n such that square root(18*n*34) is an integer? Answered by Penny Nom. 





Product of Two Integers 
20080625 

From devin: two consecutive integer have a product of 240. what are they Answered by Penny Nom. 





Two consecutive negative even numbers 
20080603 

From Chelsea: The sum of the squares of two consecutive negative even numbers is 100. Find the integers, Answered by Penny Nom. 





Two consecutive odd numbers 
20080401 

From prinsilla: of all pairs of consecutive odd integers whose sum is greater than 75. find the pair whose sum is least? Answered by Stephen La Rocque. 





Two consecutive odd integers 
20080324 

From Jarrod: the sum of two consecutive odd integers is 24. Find the two integers Answered by Stephen La Rocque. 





Two consecutive odd positive integers 
20080312 

From Sarah: The sum of the squares of two consecutive odd positive integers is 74. What are th integers? Answered by Penny Nom. 





3 consecutive odd integers 
20080228 

From Pat: For 3 consecutive odd integers, twice the first integer, plus 5 more than the second integer, plus three less than four times the third integer equals 85. Find the 3 consecutive odd integers. Answered by Penny Nom. 





The sign of the quotient of two integers 
20080201 

From michelle: without actually dividing, how can you decide whether the quotient of two integers is A. positive B. negative C. 0? Answered by Penny Nom. 





Three consecutive odd integers 
20080124 

From daniel: find three consecutive odd integers such that three times the second minus the third is 11 more than the first.
help! i have x+1, x+3, x+5 as my 3 odd integers is this correct its been a while. Answered by Penny Nom. 





Integers in sports 
20071130 

From Tariana: hey i have a project to do and i was wondering , What sports use integers? Answered by Penny Nom and Victoria West. 





the sum of two consecutive integers is 51 
20071017 

From Keira: the sum of two consecutive integers is 51 Answered by Penny Nom. 





Four consecutive integers 
20070928 

From Joshua: We were given a question that involved consecutive integers. I can not seem to solve this question and I am the top student in my class.The question states: Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91. How do you solve this question? Thank you very much for your support. Answered by Penny Nom, Stephen la Rocque and Claude Tardif. 





A question about integers 
20070824 

From Jerry: Does there exist a positive integer such that when it is written in base 10 and its leftmost digit is crossed out, the new number is 56 times less than the original number? Answered by Stephen La Rocque and Penny Nom. 





The sum of two or more consecutive integers 
20070426 

From nana: some numbers can be written as the sum of two or more consecutive integers(we consider positive integers only)
other number (eg. 4) cannot be express in this way.
let us call a number which can be expressed in this way a SOALTCI( sum of at least two consecutive integers)
a). list the first few SOALTCI and conjecture the general formula.
b). Prove that any number of the given form(in your answer (a)) is a SOALTCI Answered by Penny Nom. 





x^3 + y^4 = z^5 
20070227 

From Mike: Is there a known solution to the equation: x^3 + y^4 = z^5? This is not for marks. Just a curiosity. Thank you for your time. Answered by Stephen La Rocque. 





An even positive integer cubed minus four times the number 
20070207 

From Rachael: I can't figure out the proof or the method to get the proof for this question: any even positive integer cubed minus four times the number is divisible by 48 Answered by Haley Ess and Penny Nom. 





11^n +22^n = 55^n 
20070129 

From Ankit: 11^n +22^n = 55^n
find the value of n? Answered by Penny Nom. 





Three consecutive odd integers 
20070108 

From Emma: Find three consecutive odd integers such that the sum of the first and second is 27 less than 3 times the third. Answered by Stephen La Rocque. 





Twice the smaller of two consecutive integers is the larger increased by 5. 
20070108 

From Evan: Twice the smaller of two consecutive integers is the larger increased by 5. find the integers. Answered by Stephen La Rocque and Penny Nom. 





The Pythagorean theorem 
20061212 

From Beth: In a pythagorean theorem can the sides of a right triangle be three consecutive odd integers Answered by Stephen La Rocque. 





The sum of 2000 consecutive integers is 1000 
20061029 

From Matias: if the sum of 2000 consecutive integers is 1000, then the sum digits of the greatest of these 2000 integers is? Answered by Penny Nom. 





Three consecutive integers 
20061029 

From Jimmy: Basically i want to know how you prove that the product of any 3 consecutive integers is a multiple of 6 Answered by Stephen La Rocque. 





Onequarter of all 3subsets of the integers 1,2,3....,m contain the integer 5 
20061009 

From Hina: If onequarter of all 3subsets of the integers 1,2,3....,m contain the integer 5, determine the value of m. Answered by Steve La Rocque and Claude Tardif. 





What is the radius of the sphere? 
20060517 

From Jimmy: The surface area and volume of a sphere are both equal to the product of 4digit whole numbers and pi. What is the radius of the sphere? Answered by Stephen La Rocque. 





How many children were there? 
20060514 

From Geecee: At a local village gala, the entire population turned up, 500 people. The event raised £3,000. Tickets were priced as follows: £7.48 men, £7.12 women and £0.45 children.
How many children were there? Answered by Stephen La Rocque. 





Divide the product of three consecutive positive integers by their mean 
20060312 

From Sandy: When I divided the product of three consecutive positive integers by their mean, I got 99. What is the smallest of the three numbers? Answered by Stephen La Rocque. 





Two consecutive even integers 
20060311 

From Cheryl: Find two consecutive even integers that have a sum of 450
Answered by Stephen La Rocque. 





Find two consecutive integers whose product is 182 
20060209 

From Anthony: Find two consecutive integers whose product is 182 Answered by Steve La Rocque. 





Counting digits 
20060130 

From Cynthia: I would like to know the easiest way to calculate the
total numbers of digits used by a printer to number the pages of a book from 1 to 250. Answered by Penny Nom. 





More on the origin of integers 
20051220 

From A student: have a math extra credit project and we have to go online and look up the origin of integers and I can't find it anywhere do you know?????? Answered by Harley Weston. 





Tables with perfect squares 
20051130 

From Craig: A table consists of eleven columns. Reading across the first row of the table we find the numbers 1991, 1992, 1993,..., 2000, 2001. In the other rows, each entry in the table is 13 greater than the entry above it, and the table continues indefinitely. If a vertical column is chosen at random, then the probability of that column containing a perfect square is: Answered by Claude Tardif. 





The sum of n consecutive integers 
20051127 

From Craig:
If 875 is expressed as the sum of n consecutive integers (n > 1), then the number
of possible values of n is?
Possible Answers:
A) 15
B) 8
C) 7
D) 16
E) 4
Answered by Penny Nom. 





When will x^2+xy+(yx) be even? 
20051108 

From Lana: If x and y are integers, when will x squared+xy+(yx) be even? Answered by Penny Nom. 





Divisibility by each of the first ten counting numbers 
20051017 

From Simon: determine smallest positive integer that is divisible by each of the first ten counting numbers Answered by Penny Nom. 





Whole numbers 
20051010 

From Kirk: Can the sum of two or more whole numbers be less than any of those numbers? Answered by Penny Nom. 





Can one place 15 integers around a circle... 
20050820 

From Hernan: Can one place 15 integers around a circle so that the sum of every 4 consecutive numbers is equal either to 1 or 3? Answered by Claude Tardif. 





Proof by induction? 
20050810 

From Peter:
I am a lecturer and am having a problem with the following Proof by
Induction.
If
(N x N x N x N) + (4 x N x N x N) + (3 x N x N) + (N) = 4000
Prove that N is even!
Answered by Chris Fisher and Penny Nom. 





how do i round up 9.6 to the nears ones 
20050809 

From Carlos: how do i round up 9.6 to the nears ones Answered by Penny Nom. 





Adding consecutive integers 
20050513 

From Yas: i need some help with my work which is to investigating sums of consecutive numbers for example: 15= 4+5+6 and 15=1+2+3+4+5 Answered by Penny Nom. 





The least integer of a set of consecutive integers 
20050419 

From Lucia: The least integer of a set of consecutive integers is 25. If the sum of these integers is 26, how many integers are in the set? Answered by Penny Nom. 





1/x + 1/y = 2/31 
20041201 

From matt: I have this problem which I think is a bit more tricky than usual.
x and y are positive integers.
1/x + 1/y = 2/31 Answered by Claude Tardif. 





Integers 
20040610 

From A parent: I have an odd 3 digit product. My factors are a 1digit number and either or 2 or 3digit number. My factors are odd, but neither is 1. Find my factors and my product.
There is one answer. What is it? Answered by Penny Nom. 





The sum of some positive integers 
20040607 

From A student: Find the sum of all positive integers not greater than 10000 that are divisible by neither 3 nor 7. Answered by Penny Nom. 





The product of any n consecutive integers 
20040118 

From Fazia: I have to prove that the product of any n consecutive integers is divisible by n!(eg:the product of five consecutive integers is divisible by 5!) It's easy enough to plug in numbers and prove it is true, but i'm finding it difficult to come up with a proper proof. Answered by Claude Tardif. 





Two consecutive negative integers 
20040117 

From Amanda: Find two consecutive negative intergers whose product is 182. Answered by Penny Nom. 





Why is the letter J used for the integers? 
20040113 

From Amanda: Why is the letter J used to represent intergers as a symbol? Answered by Penny Nom. 





1/x + 1/y = 5/12 
20031030 

From Ben: 1/x +1/y =5/12, what is the sum of x and y? Answered by Penny Nom. 





Consecutive integers 
20030907 

From Amy: I was wondering if there was a proper way to write the solution to a problem requiring consecutive integers? Is it okay to write the solution as 5,4,3,2,1 or must it be written as 1,2,3,4,5? Answered by Penny Nom. 





Two row arrays 
20030903 

From Madalyn: My question is, what are #'s that can not be arranged in two row arrays called? Answered by Penny Nom. 





positive multiples of 10 that are the sum of four consecutive integers 
20030501 

From Taurus: How many positive multiples of 10 that are less than 1000 are the sum of four consecutive integers? Answered by Penny Nom. 





The product of four consecutive integers is 3024. 
20030425 

From pillar: The product of four consecutive integers is 3024. What are those numbers. Answered by Penny Nom. 





How many hits? 
20030406 

From Jack:
My name is Jack. I'm a uncle. Student is in the 5th grade email is above. If a baseball player at sping training had a good season with the following: one seventh of his hits were doubles. 12.5% of his hits were home runs. But didn't have any triples. How many hits did he have? Can you give me an explanation of you solved the problem. Answered by Penny Nom. 





Can twice a square be a square? 
20030325 

From Mike: The other day it occurred to some students that they could think of no square number which is an integer, which can be divided into two equal square numbers which are intergers, Or put another way, no squared integer when doubled can equal another square integer. For example 5 squared plus 5 squared is 50, but 50 is not a square number. Answered by Walter Whiteley and Claude Tardif. 





The origin of integers 
20030319 

From Travis: What are the real life usages of integers? Also what is the origin of integers? Answered by Harley Weston. 





(x^{y})^{z} = 64 
20030226 

From Melissa: How many ordered triples of positive intergers (xyz) satisfy (x[raised to the y])raised to the z = 64? Answered by Penny Nom. 





Three consecutive positive intergers 
20030209 

From Yew: Prove that when we multiply any consecutive positive intergers, the result is always divisible by 6.
ex. (7)(8)(9) = 504 = 6 (84) Answered by Penny Nom. 





The cousin of Sally's sister's boyfriend 
20030123 

From Michael: Sally went to a farm to buy eggs. Returning home, she gave half of them to her sister who, in turn, gave a third of those she had gotten to her boyfriend. The latter, after eating one third of the eggs that he had gotten, gave the rest to his cousin. Given that each egg weighs 70 grams, that Sally cannot carry more than 2.5kg, and that the eggs were raw, calculate how many eggs the cousin of Sally's sister's boyfriend received. Answered by Penny Nom. 





Integer arithmetic 
20021205 

From A student: Would you please help me with a question?
I am just learning about integers. Can you show me in a way I might understand....My teacher can tell me what is required to do the math, but it just doesn't make sence to me.
(+4)  (3) =+7
Why is the answer not +1 Answered by Diane Hanson. 





65,125 
20021204 

From Brittany: I am a threedigit number.When you reverse my digits,a larger number is formed.the product of me and the new number is 65,125.What number am I. Answered by Chris Fisher and Claude Tardif. 





Integers in real life 
20021015 

From Rica: What are the real life usages of integers? Answered by Peny Nom. 





Relatively prime 
20021004 

From Natasha: I really need help with this middle level math question. My little brother is asking me and I have no clue what the answer is. Explain what it means when two numbers are negatively prime. (?) Answered by Kathy Nolan and Penny Nom. 





7+8+9+...+1000 
20020911 

From Shirley: My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers? Answered by Penny Nom. 





The sum of the first one hundred even numbers 
20020910 

From Arthur: What is the sum of the first one hundred even numbers? Answered by Penny Nom. 





Subsets of the Real Number System 
20020907 

From Christine: In looking for a French equivalent of the word "integer", I found that the word seems not to actually exist in French, and that Canadian schools use the term "natural number" to describe what we have been trained to call "whole numbers," while using the term "whole number" to describe what we have been trained to call "integers." Answered by Claude Tardif. 





Express 5120 as a sum of consecutive numbers 
20020825 

From Todd: Express 5120 as a sum of more than 1 consecutive number. Answered by Leeanne Boehm. 





A degree 5 polynomial 
20020217 

From Carla: Write an equation for a polynomial of degree 5 given the following zeros: 7+3i, 2+sqrt(13), 6 Answered by Penny Nom. 





Why do integers have the symbol of Z? 
20020111 

From Stephanie: Why do integers have the symbol of Z? Natural numbers have the symbol of N, whole numbers have the symbol of W. Our professor has asked us to find out why the letter Z is represented for integers. Answered by Penny Nom. 





Integers 
20011202 

From Alison: How do you use integers in your everday life? Answered by Harley Weston. 





Odd plus even is odd 
20011014 

From James: Why is the sum of an odd number and an even number always odd? Answered by Peny Nom. 





Integers 
20010909 

From A student: I am a Grade 9 student from Ontario Canada who has never understood how to do integers very well. I was wondering if you would be able to either send me some sites that will tell me how to calculate them in a simple way or if you would be able to write me back and give me some pointers. Answered by Leeanne Boehm. 





I have 6 digits. 
20010906 

From Kristan: I have 6 digits. My hundred thousands is 1 less than my 1 digit, 8 greater than my thousands digit, twice my tens digit, and 4 times my hundreds digit. My ten thousands digit is 0. What # am I? Answered by Penny Nom. 





Three goldfish 
20010530 

From Nathan: A man has three goldfish. When the youngest goldfish was born, the oldest fish was three times the middle fish's age. Nine years ago the oldest fish's age was the sum of the two other fish's ages. How old are the three goldfish? Answered by Penny Nom. 





A sequence defined recursively 
20010501 

From A student: A sequence s is defined recursively as follows: s_{0}=1 s_{1}=2 s_{k}=2s_{k2} for all integers  Compute s2,s3,s4... to guess an explicit formula for the sequence sk. Answered by Penny Nom. 





Dominos 
20010428 

From Mark: A standard dominoe set consists of 28 pieces, from doublezero to doublesix  Is it possible to arrange all those pieces in a straight line in such a way that the dots of any pair of adjacent pieces match? Please include picture
 Is it possible to arrange them in a circle and still meet the conditions in 1?
Answered by Claude Tardif. 





x^5 + y^5 + z^5 = w^5 
20010111 

From Samuel Brown: x^{5} + y^{5} + z^{5} = w^{5} I have no idea whether or not this is possible. Answered by Claude Tardif. 





Integral solutions 
20001120 

From David: determine all pairs of integers (x,y) which satisfy the equation 6x^{2}  3xy  13x + 5y = 11 I got y= (6x^{2}13x+11)/(3x5) and i don't konw how to continue Answered by Claude Tardif. 





Buying art supplies 
20000918 

From Travis: An art teacher buys exactly 100 items at this sale, and the total cost before tax is $100. She buys at least one of each item. How many of each item does she buy? Markers $0.50 Sketch Pads $3.00 Paint Sets $10.00 Answered by Denis Hanson. 





1 + 2 + 3 + ... + 50 
20000914 

From Vicki Charron: How can you calculate the total of the numbers one through fifty, without adding up the individual numbers? Answered by Penny Nom. 





n^{3} + 2n^{2} is a square 
20000904 

From David Xiao: determine the smallest positive integers, n , which satisfies the equation n^{3} + 2n^{2} = b where b is the square of an odd integer Answered by Harley Weston. 





Three consecutive odd integers 
20000818 

From Wallace: A sixdigit integer XYXYXY, where X and Y are digits is equal to five times the product of three consecutive odd integers. Determine these three odd integers. Answered by Paul Betts. 





(mn + m + n)/(m^2 + n^2) = 1 
20000724 

From William: Find all pair of positive integers m and n such that mn + m + n divides m^{2} + n^{2} = 1. Answered by Peny Nom. 





Natural numbers 
20000412 

From Sara: What is a natural number??? Answered by Penny Nom. 





Rationals, irrationals and integers 
20000314 

From Erin McKeon: Why does the letter J represent the set of integers, the letter Q represent a set of rational numbers and the letter P represent a set of irrational numbers? What do each of these letters stand for? Answered by Harley Weston. 





An integer maxmin problem 
20000313 

From Paul Servic: Maximize Q = xy^{ 2} where x and y are positive integers such that x + y^{ 2} = 4 Answered by Penny Nom. 





Is zero an even or odd number? 
20000206 

From Christian Hansen: On a list I run, someone posted that 02022000 was the first date since 2808888 where all the digits were even. Of course, this provoked a discussion of whether zero was odd, or even, or neither. I remember reading that, for symmetry's sake, it is considered by mathematicians to be even. Any thoughts? Answered by Patrick Maidorn. 





Whole numbers 
19991202 

From Patty: I'm in a 5th grade class, please explaine what whole numbers are..... Answered by Penny Nom. 





The greatest possible difference 
19990917 

From Denea Hugunin: Use each of the digits 1 to 5 once to make a 2 digit number and a three digit number that the greatest possible difference. Answered by Penny Nom. 





111...1222...2 
19990811 

From Brad Goorman: Let N = 111...1222...2, where there are 1999 digits of 1 followed by 1999 digits of 2. Express N as the product of four integers, each of them greater than 1. Answered by Penny Nom. 





Evens and odds 
19990504 

From Emily Hays: My name is Emily Hays, I am in the 6th grade and my teacher gave me some extra probelms to see if I could solve them. She can't find the KEY and I can't figure out the probelm so she suggested I email you guys to see if you could help us. Here's the Problem: The numbers 1,2,3...,1999 are written on the blackboard in the classroom. Evertime the teacher enters the room he chooses two numbers on the blackboard, say a & b, with a> or equal to b, then he erases them and writes the difference ab somewhere on the blackboard. After this procedure is carried on 1998 times, there will be only one number left on the blackboard. Prove the last remaining number must be even. I hope you can help us! Answered by Chris Fisher and Harley Weston. 





A Place Value Curiosity 
19980525 

From Ed: I was visiting with an elderly gentleman this afternoon. He showed me this curiosity and then asked if I could explain it to him. Can you provide an explanation of why the 9 or multiple of 9 keeps occurring in this procedure? Choose any number, say 125 and add the digits to get 8. subtract the 8 from the 125 and the result is 117. Add the digits in 117 to get 9. Subtract the 9 from the 117 to get 108. Add the digits in 108 to get 9. If this procedure continues a 9 or a multiple of 9 reoccurs. What is the mathematical explanation behind this happening? Answered by Denis Hanson. 





x^2 = ...444 
19980223 

From James Bauer: What is the first interger that when squared ends in three 4's? (ex. x^2 = ...444) Prove that there are no intergers that when squared end in four 4's (ex. x^2 = ...4444) Answered by Penny Nom. 





Integer Problems. 
19970915 

From Eric Kowalsky: I have some intergers I can't solve. Please help me solve them! Please show me how you got the answer. 5(4)[3(6)+(3)4(2(4)7)]+3(8)=
 2[73(4)+52(1)]+3(6+8)=
 4[6(27)5(7+2)]=
 7(4)2[3(4+6)+6(73(4))]
P.S. Thank you very much. Answered by Harley Weston. 





When is ( n^3+1)/(mn1) an integer? 
19970211 

From Ronald Lui: Determine all ordered pairs (m,n) of positive integers such that ( n^3+1)/(mn1)is an integer. Answered by Richard McIntosh. 





Combien y aura t il de 9 dans la réponse? 
20000617 

From Marie: J'ai lu une énigme mais je n'ai pas la réponse."si l'on divise 123 456 789 par 999 999 999, combien y aura t il de 9 dans la réponse?" Answered by Claude Tardif. 

