A generalization of Fermat's little theorem. Euler published a proof of the following more general theorem in 1736. Let 
denote the totient function.
Then
 |
for all 
relatively prime to 
.
Euler's Totient Theorem
See also
Chinese Hypothesis, Fermat's Little Theorem, Totient FunctionExplore with Wolfram|Alpha
References
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. https://mathworld.wolfram.com/EulersTotientTheorem.html