Euler's Totient Theorem

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Euler's Totient Theorem is a theorem closely related to his function of the same name.


Let $\phi(n)$ be Euler's totient function. If ${a}$ is an integer and $m$ is a positive integer relatively prime to $a$, then ${a}^{\phi (m)}\equiv 1 \pmod {m}$.


This theorem is credited to Leonhard Euler. It is a generalization of Fermat's Little Theorem, which specifies that ${m}$ is prime. For this reason it is known as Euler's generalization and Fermat-Euler as well.

See also

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