Carmichael Function

In number theory, the Carmichael function of a positive integer n, written lambda of n, is the smallest positive integer m such that a to the m is congruent to one modulo n for every integer a coprime to n. In algebraic terms it is the exponent of the multiplicative group of integers modulo n, a finite abelian group guaranteed to contain an element, called a primitive lambda root, whose order equals that exponent. Named after the American mathematician Robert Carmichael, who defined it in 1910, it is also known as Carmichael's lambda function, the reduced totient function, or the least universal exponent function, and because the order of any element of a group divides the order of the group, lambda of n always divides Euler's totient function of n.