Group of units modulo prime power is cyclic

Statement

Let $p$ be a prime, $k$ be an integer.

The group of units modulo $(\mathbb{Z}/p^k\mathbb{Z}{)}^{\times }$ is cyclic.

Proof

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Weaker statement

• Group of units modulo prime is cyclic is the case $k=1$.

See also

• Group of units modulo n
• Group of units modulo two times prime power is cyclic