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

Theorem
Let $\Q_p$ be the $p$-adic numbers for some prime $p \ne 2$.

Let $\Q_p^\times$ denote the set of invertible elements of $\Q_p$.

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

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