Category:Characterization of Integer has Square Root in P-adic Integers

This category contains pages concerning Characterization of Integer has Square Root in P-adic Integers:

Let $\Z_p$ be the $p$-adic integers for some prime $p \ne 2$.

Let $a \in Z$ be an integer such that $p \nmid a$.

Then:

$\exists x \in \Z_p : x^2 = a$

if and only if

$a$ is a quadratic residue of $p$.