Quotient Group of Quadratic Residues Modulo p of P-adic Units/Corollary

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

Let $\Z_p^\times$ denote the set of $p$-adic units.

Let $\paren{\Z_p^\times}^2 = \set{a^2 : a \in \Z_p^\times}$

Then:
 * $\Z_p^\times / \paren{\Z_p^\times}^2$ is isomorphic to $\Z / 2\Z \oplus \Z / 2\Z$