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.

Let the 3 sides be A = u^2-v^2, B = 2uv, C = u^2+v^2 (Euclid) Then B+C=u^2+2uv+v^2=(u+v)^2. Since the triplet is primitive, both A and C must be odd; hence u and v are of opposite parities and (u+v)^2 is also odd. (1) And (A+C)/2=(u^2-v^2+u^2+v^2)/2=(2u^2)/2, namely u^2.(2)