Euler's 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

$$a^{\phi(n)}\equiv 1\ \left({{\rm mod\ } {n}}\right)$$

for all $a$ Relatively Prime to $n$.

See also Chinese Hypothesis, Euler's Displacement Theorem, Euler's Distribution Theorem, Fermat's Little Theorem, Totient Function

References

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 21 and 23-25, 1993.