Difference between revisions of "Euler's Totient Theorem"

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

Revision as of 20:34, 24 June 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.

See also

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