Art of Problem Solving
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Euler's Totient Theorem: Difference between revisions

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=== Credit ===
=== Credit ===


This theorem is credited to [[Leonhard Euler]].
This theorem is credited to [[Leonhard Euler]].  It is a generalization of [[Fermat's Little Theorem]], which specifies that <math>{m}</math> is prime.


=== See also ===
=== See also ===
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* [[Modular arithmetic]]
* [[Modular arithmetic]]
* [[Euler's totient function]]
* [[Euler's totient function]]
* [[Fermat's Little Theorem]]

Revision as of 18:09, 18 June 2006

Statement

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

Credit

This theorem is credited to Leonhard Euler. It is a generalization of Fermat's Little Theorem, which specifies that ${m}$ is prime.

See also