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> | + | 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 19:34, 24 June 2006
Statement
Let 
be Euler's totient function. If 
is an integer and 
is a positive integer relatively prime to 
, then 
.
Credit
This theorem is credited to Leonhard Euler. It is a generalization of Fermat's Little Theorem, which specifies that 
is prime.
