The triangle with sides 3, 4, and 5, is the smallest integer sided pythagorean triangle. Can you prove that in every such triangle:

• at least one of its sides must be multiple of 3?
• at least one of its sides must be multiple of 4?
• at least one of its sides must be multiple of 5?

All pythagorean triples can be generated with formula 2MN,M^2-N^2,M^2+N^2 where M and N are relatively primes and M>N
It's pretty easy to see that every one of those three is divisible by either 3,4 or 5 depending on wether M and/or N are odd or even numbers (Can be proved easily with induction)
Since all of them are divisible by 3,4 or 5 every such triangle must have sides in the way described in this problem.
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Edited on July 3, 2006, 1:57 pm

Posted by atheron on 2006-07-03 13:56:09