# Euler's totient function ## Metadata **Status**:: #x **Zettel**:: #zettel/fleeting **Created**:: [[2024-03-06]] **URL**:: [wikipedia.org](https://en.wikipedia.org/wiki/Euler%27s_totient_function) **Highlights**:: [[Wikipedia Authors - Euler's Totient Function (Highlights)]] ## Synopsis **Euler's totient function** counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter *phi* as $\varphi (n)$ or $\phi(n)$, and may also be called **Euler's phi function**. In other words, it is the number of integers k in the range 1 ≤ _k_ ≤ _n_ for which the greatest common divisor gcd(_n_, _k_) is equal to 1.