Quotient Group of Quadratic Residues Modulo 2 of 2-adic Units/Corollary

Theorem
Let $\Z_2$ be the $2$-adic integerss.

Let $\Z_2^\times$ denote the set of $2$-adic units.

Let $\paren{\Z_2^\times}^2 = \set{a^2 : a \in \Z_2^\times}$

Then:
 * $\Z_2^\times / \paren{\Z_2^\times}^2$ is isomorphic to $\Z / 2\Z \oplus \Z / 2\Z \oplus \Z / 2\Z$