I am a freshman studying computer science, and I am supposed to solve this problem for my '(introduction to) elementary number theory' course. Could someone give me a hint or two on how to solve the following problem?
Prove that: If $p$ is a prime number ($p=4\cdot n-1$ where $n$ is a natural number) and $x^2+y^2\equiv 0 \pmod{p} $, then $x\equiv 0 \pmod{p}$ and $y\equiv 0 \pmod{p}$.