







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. 





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. 





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. 





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. 





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. 





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. 





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. 

