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Euler's Totient Theorem

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(Redirected from Fermat-Euler Theorem)

Euler's Totient Theorem is a theorem closely related to his function of the same name.

Theorem

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

Want to learn how to tackle those tough AMC/AIME/Olympiad algebra problems? Check out Art of Problem Solving's Intermediate Algebra by Richard Rusczyk and Mathew Crawford. Over 1600 problems!
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