grandes-ecoles 2022 Q7.6

grandes-ecoles · France · x-ens-maths-d__mp Number Theory Congruence Reasoning and Parity Arguments

Let $p$ be a prime number. Show that there exists $h\in\mathbb{Z}/p\mathbb{Z}$ such that $h^2=-1$ if and only if $p=2$ or $p\equiv 1\bmod 4$.

Let $p$ be a prime number. Show that there exists $h\in\mathbb{Z}/p\mathbb{Z}$ such that $h^2=-1$ if and only if $p=2$ or $p\equiv 1\bmod 4$.