Difference between revisions of "Euler's Totient Theorem"

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=== Credit ===
 
=== 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.
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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 ===
 
=== See also ===

Revision as of 13:41, 4 November 2006

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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