Totative

In number theory, a totative of a given positive integer $n$ is an integer $k$ such that $0 < k \leq n$ 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 proved by Bob Vaughan and Hugh Montgomery.