# Euler's totient function

Last edited: 2026-01-28

Euler’s totient function

For a natural number $n \in \mathbb{N}$ define Euler’s totient function as

$$\phi(n) = \big \vert \left \{x \in \mathbb{N} \ \vert \ 0 < x \leq n, \ \gcd(x, n) = 1 \right \} \big \vert.$$

# Theory

This is normally calculated using Eulers product formula (totient function) . Statement