Totative


In number theory, a totative of a given positive integer is an integer such that and is coprime to . Euler's totient function φ counts the number of totatives of n. The totatives under multiplication modulo n form the multiplicative group of integers modulo n.

Distribution

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.