How can I prove that the multiplicative group $G:=\{m\in\mathbb Z_{2^n}:m\equiv 1 \mod 4\}$ is cyclic? I tried claiming that $G=\langle5\rangle$ but failed.
2026-03-29 12:04:40.1774785880
$\{m\in\mathbb Z_{2^n}:m\equiv 1 \mod 4\}$ is cyclic
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