# Modular Arithmetic/Euler's Theorem

If ${\displaystyle \alpha }$ and ${\displaystyle \beta }$ are positive coprime integers, then,
${\displaystyle \alpha ^{\phi (\beta )}\equiv 1{\pmod {\beta }}}$
${\displaystyle \phi }$ denotes Euler's totient function. ${\displaystyle \phi (\beta )}$ gives the number of positive integers up to ${\displaystyle \beta }$ that are relatively prime to ${\displaystyle \beta }$.