Euler's theorem

In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that if n and a are coprime positive integers, then a raised to the power of the totient of n is congruent to one, modulo n, or: The converse of Euler's theorem is also true: if the above congruence is true, then and must be coprime. The theorem is a generalization of Fermat's little theorem, and is further generalized by Carmichael's theorem. In general, when reducing a power of modulo (where and are coprime), one needs to work modulo in the exponent of : if , then .

Euler's theorem

In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that if n and a are coprime positive integers, then a raised to the power of the totient of n is congruent to one, modulo n, or: The converse of Euler's theorem is also true: if the above congruence is true, then and must be coprime. The theorem is a generalization of Fermat's little theorem, and is further generalized by Carmichael's theorem. In general, when reducing a power of modulo (where and are coprime), one needs to work modulo in the exponent of : if , then .