Prove: The integer p-1 is a quadratic residue of an odd prime p if and only if p congruent 1 ( mod4).

Question

Prove: The integer p-1 is a quadratic residue of an odd prime p if and only if p congruent 1 ( mod4). enter image description here That’s right?!

Answer 1

If you tried solving it using Euler's criterion, then you are basically looking for an answer to "When is $\frac{p-1}2$ even?" That happens exactly when $p-1$ is divisible by $4$, which is to say $p\equiv 1\pmod4$.