Modular Arithmetic/Euler's Theorem

Euler's Theorem

If $\alpha$ and $\beta$ are positive coprime integers, then,

\alpha ^{\phi (\beta )}\equiv 1{\pmod {\beta }}

\phi

denotes Euler's totient function.

\phi (\beta )

gives the number of positive integers up to

\beta

that are relatively prime to

\beta

.

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