Abstract Algebra: Theory and Applications · Problem 2.4.21

Groups — Thomas Judson

Mathematics — Abstract Algebra · pythagorean-parity

Problem

Suppose that

a, b, r, s

are pairwise relatively prime and that

a^2 + b^2 = r^2

a^2 - b^2 = s^2.

Prove that

a

r

, and

s

are odd and

b

is even.