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 $\beta$.