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# State/Fermat Euler theorem

Theorem: (Fermat-Euler theorem) Suppose that $m$ is a positive integer. Suppose that $a \in \ZZ$ and $GCD(a,m) = 1$. Then, $$\bar a^{\phi(m)} = \bar 1, \mbox{ modulo } m,$$ where $\phi(m)$ denotes the totient of $m$.

## Logical Connections

This statement logically relies on the following definitions and statements: Def/Residue, Def/Totient, Def/Invertible residue, State/Relative primality to the modulus is equivalent to invertibility of a residue, State/Products of invertible residues are invertible, Def/Permutation

The following statements and definitions rely on the material of this page: State/Fermats little theorem

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