Difference between revisions of "Euler's Totient Theorem"

m (Euler's totient theorem moved to Euler's Totient Theorem: Capitalization policy is currently to capitalize names of theorems, I believe (see [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=97741 here]).)
m (See also)
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* [[Modular arithmetic]]
 
* [[Modular arithmetic]]
 
* [[Euler's totient function]]
 
* [[Euler's totient function]]
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* [[Carmichael function]]

Revision as of 19:43, 26 January 2007

Statement

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

Credit

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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