IR-TST 2004 Problem 2

Suppose that $p$ is a prime number. Prove that the equation $x^2-py^2=-1$ has a solution if and only if $p\equiv1\pmod 4$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.