2134/761 R.R. Hall R.R. Hall Peter Shiu Peter Shiu The distribution of totatives Loughborough University 2006 Erdos Lehmer Mathematics Totatives Mathematical Sciences not elsewhere classified 2006-02-06 16:38:54 Preprint https://repository.lboro.ac.uk/articles/preprint/The_distribution_of_totatives/9383756 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.