Difference between revisions of "Fermat's Little Theorem"

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Note: This theorem is a special case of [[Euler's totient theorem]].
 
Note: This theorem is a special case of [[Euler's totient theorem]].
  
== Corollary ==
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=== Corollary ===
  
 
A frequently used corolary of Fermat's little theorem is <math> a^p \equiv a \pmod {p}</math>.
 
A frequently used corolary of Fermat's little theorem is <math> a^p \equiv a \pmod {p}</math>.

Revision as of 11:57, 18 June 2006

Statement

If ${a}$ is an integer and ${p}$ is a prime number, then $a^{p-1}\equiv 1 \pmod {p}$.

Note: This theorem is a special case of Euler's totient theorem.

Corollary

A frequently used corolary of Fermat's little theorem is $a^p \equiv a \pmod {p}$. As you can see, it is derived by multipling both sides of the theorem by a.

Credit

This theorem is credited to Pierre Fermat.

See also

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