Question

Let s and t be odd integers with x > t >= 1 and gcd (s,t) = 1. Prove that st, (s^2-t^2)/2, and (s^2+t^2)/2 are pairwise relatively prime.

Answer 1

FYI, those three numbers are the formulas for generating primitive pythagorean triples, with a = st, b = (s^2-t^2)/2, and c = (s^2+t^2)/2. Also, a will be odd and b will be even.

Answer 2

maybe assume they are not and derive a contradiction