Question 543124
By looking at certain right triangles such as 3-4-5, 5-12-13, 8-15-17, etc., we can conjecture that a+b+c is always even. To prove this, suppose that the opposite was true, that a+b+c could be odd. If this is so, then either all three are odd (contradiction, because odd + odd is not equal to odd) or exactly one of the three is odd (also contradiction because even + odd is never even, even + even is never odd). Hence a+b+c is even.


Tip: Instead of using odd + odd or even + even, use something like "(2k+1) + (2m+1)" or go even simpler and use modular arithmetic (e.g. 1+1 is never congruent to 1 mod 2).