Let $a, b,c,d$ be positive integers such that $ac+bd$ is divisible by $a^2 +b^2$. Prove that $gcd(c^2 + d^2, a^2 + b^2) > 1$. Trần Nam Dũng
Source: 2015 Saudi Arabia IMO TST IV p1
Tags: number theory, divides, divisible, GCD
Let $a, b,c,d$ be positive integers such that $ac+bd$ is divisible by $a^2 +b^2$. Prove that $gcd(c^2 + d^2, a^2 + b^2) > 1$. Trần Nam Dũng