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Composite triples 2006-01-24
From Laeah:
question 1 Find the smallest integer n such that n+1, n+2,and n+3 are all composites.

question 2 If n = 5! +1, show that n+1, n+2, and n+3 are all composite.

question 3 Find the sequence of 1000 consecutive composite numbers.

Answered by Penny Nom.
Triangles with integer sides 2005-11-04
From Tammy:
I am trying to find another pair of integer sided isosceles triangles, not the same as the ones listed below, with equal areas. (5,5,8) (5,5,6)
Answered by Chri Fisher.
Odd Pythagorean triples 2003-10-23
From Kathleen:
in a triple can a and b be odd numbers
Answered by Penny Nom.
The median with ties 2002-02-27
From Marcel:
What, exactly, is the proper way to determine the median of a set of numbers when doubles or triples of a number are part of that set? Do the doubles count as two and the triples three, or does each count only as one toward determining the median.
Answered by Harley Wston.
Pythagoras & magic squares 2001-10-09
From John:
My grandson became intrigued when he recently 'did' Pythagoras at elementary school. He was particularly interested in the 3-4-5 triangle, and the fact that his teacher told him there was also a 5-12-13 triangle, i.e. both right-angled triangles with whole numbers for all three sides. He noticed that the shortest sides in the two triangles were consecutive odd numbers, 3 & 5, and he asked me if other right angled triangles existed, perhaps 'built' on 7, 9, 11 and so on.

I didn't know where to start on this, but, after trying all sorts of ideas, we discovered that the centre number in a 3-order 'magic square' was 5, i.e. (1+9)/2, and that 4 was 'one less'. Since the centre number in a 5-order 'magic square' was 13 and that 12 was 'one less' he reckoned that he should test whether a 7-order square would also generate a right-angled triangle for him. He found that 7-24-25, arrived at by the above process, also worked! He tried a few more at random, and they all worked. He then asked me two questions I can't begin to answer ...

  1. Is there a right-angled triangle whose sides are whole numbers for every triangle whose shortest side is a whole odd number? and

  2. Is each triangle unique (or, as he put it, can you only have one whole-number-sided right-angled triangle for each triangle whose shortest side is an odd number)?

Answered by Chris Fisher.
Pythagorean triples 2000-03-01
From Bob Ross :
Could you please tell me what pythagoria triad is.I am a year 10 student.
Answered by Chris Fisher.
Pythagorean Triples. 1997-12-04
From Shameq Sayeed:
I've got a couple of problems which I hope you'll be able to solve for me.

I'm investigating pythagorean triples, and I have found a trend for the triples themselves, and thus have been able to form a general equation, i.e. a=2x+1, b=2x^2+2x, and c=b+1. Now, I sure this equation works, because I've tried it out and have come up with triples that adhere to a^2 + b^2 = c^2. But I was wondering WHY c=b+1. Is it possible to have c=b+2, and if not why not? THAT is the first problem.
Answered by Chris Fisher.




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