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The Distribution of Totatives

Published online by Cambridge University Press:  20 November 2018

R. R. Hall  and
P. Shiu
R. R. Hall
Affiliation:
Department of Mathematics, York University, Heslington, York YO1 5DD, United Kingdom, email: rrh1@york.ac.uk
P. Shiu
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom, email: P.Shiu@lboro.ac.uk
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Abstract

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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. Erdős, who made a conjecture on such distributions. We prove his conjecture by establishing a theorem on the ordering of residues.

Keywords

11A0511A0711A25Euler’s functiontotatives
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 109 - 114
Copyright
Copyright © Canadian Mathematical Society 2002

References

[1] Erdős, P., Some remarks on a paper of McCarthy. Canad. Math. Bull. 1 (1958), 71–75.Google Scholar
[2] Erdős, P., Remarks and corrections to my paper ‘Some remarks on a paper of McCarthy’. Canad. Math. Bull. 3 (1960), 127–129.Google Scholar
[3] Lehmer, D. H., The distribution of totatives. Canad. J. Math. 7 (1955), 347–357.Google Scholar
[4] McCarthy, P. J., Note on the distribution of the totatives. Amer.Math. Monthly 64 (1957), 585–586.Google Scholar