For any primitive Pythagorean triplet the following rules apply :
1. The sum of the hypotenuse and one of the legs of a PPT is a square of an odd number,
2. The arithmetic mean of the hypotenuse and the odd leg is a perfect square.

Prove it, please.

(In reply to Solution by broll)

In (1) you should mention that u and v have different parity and therefore u+v is odd.

Posted by Bractals on 2012-10-06 16:51:46