Assume that $p$ is a prime number congruent to 1 modulo 4. Let $\alpha\geq 1$. Show that there exists $j\in\mathbb{Z}/p^\alpha\mathbb{Z}$ such that $j^2=-1$.
Assume that $p$ is a prime number congruent to 1 modulo 4. Let $\alpha\geq 1$. Show that there exists $j\in\mathbb{Z}/p^\alpha\mathbb{Z}$ such that $j^2=-1$.