Problem

Source: China Southeast Math Olympiad 2014 No.1

Tags: modular arithmetic, number theory unsolved, number theory



Let $p$ be an odd prime.Positive integers $a,b,c,d$ are less than $p$,and satisfy $p|a^2+b^2$ and $p|c^2+d^2$.Prove that exactly one of $ac+bd$ and $ad+bc$ is divisible by $p$