Euler's Totient Theorem

A generalization of Fermat's little theorem. Euler published a proof of the following more general theorem in 1736. Let phi(n) denote the totient function. Then

 a^(phi(n))=1 (mod n)

for all a relatively prime to n.

See also

Chinese Hypothesis, Fermat's Little Theorem, Totient Function

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Séroul, R. "The Theorems of Fermat and Euler." §2.8 in Programming for Mathematicians. Berlin: Springer-Verlag, p. 15, 2000.Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 21 and 23-25, 1993.

Cite this as:

Weisstein, Eric W. "Euler's Totient Theorem." From MathWorld--A Wolfram Web Resource.

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