= Unit square classes of the p-adic integers
{title2=$\mathbb Z_p^\times/(\mathbb Z_p^\times)^2$}
= p-adic unit square-class group
{synonym}
For odd $p$, a <p-adic unit> is a square exactly when its residue is a square, by the <Hensel lemma>. Its unit square-class group is $C_2$. For $p=2$, a unit is a square exactly when it is congruent to one modulo eight, by the <strong form of Hensel lemma>. The four <square classes> are represented by $1,3,5,7$, giving $C_2\times C_2$.
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