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Let $\mathbb{Z}, +$ be the group integers, $\mathbb{Z}/n\mathbb{Z}, \times$ the multiplicative group of integers modulo $n$, and $\varphi(n)$ its order. Then $\varphi(n)\mathbb{Z}, +$, the additive group of multiples of $\varphi(n)$ is a subgroup of $\mathbb{Z}$. The function $f : \mathbb{Z} \rightarrow \mathbb{Z}/n\mathbb{Z} : x \mapsto a^x \mod n$ for ...

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