In number theory, a totative of a given positive integer n is an integer k such that 0 < k ≤ n and k is coprime to n. Euler's totient function φ(n) counts the number of totatives of n. The totatives under multiplication modulo n form the multiplicative group of integers modulo n. The distribution of totatives has been a subject of study.
Paul Erdős conjectured that, writing the totatives of n as the mean square gap satisfies for some constant C, and this was proven by Bob Vaughan and Hugh Montgomery.
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