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

== Theorem ==
Let <math>\phi(n)</math> be [[Euler's totient function]]. If <math>{a}</math> is an integer and <math>m</math> is a positive integer [[relatively prime]] to <math>a</math>, then <math>{a}^{\phi (m)}\equiv 1 \pmod {m}</math>.

== Credit ==

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

== See also ==

* [[Number theory]]
* [[Modular arithmetic]]
* [[Euler's totient function]]
* [[Carmichael function]]

[[Category:Number theory]]

[[Category:Theorems]]