In number theory, a totative of a given positive integer is an integer such that and is coprime to . Euler's totient function ÃÂ(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 Erdà Âs 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.