In number theory, the Carmichael function of a positive integer $n$, denoted ${\displaystyle \lambda (n)}$, is defined as the smallest positive integer $m$ such that $a^m \equiv 1\pmod n$ for every integer a that is coprime to n. In more algebraic terms, it defines the exponent of the multiplicative group of integers modulo n. The Carmichael function is also known as the reduced totient function or the least universal exponent function, and is sometimes also denoted ${\displaystyle \psi (n)}$.