The distribution of totatives

2006-02-06T16:38:54Z (GMT) by R.R. Hall Peter Shiu
D. H. Lehmer initiated the study of the distribution of totatives, which are numbers coprime with a given integer. This led to various problems considered by P. Erdos, who made a conjecture on such distributions. We clarify results due to Erdos and prove his conjecture by establishing a theorem on the ordering of residues.