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The Distribution of Totatives

  Published:2002-03-01
 Printed: Mar 2002
  • R. R. Hall
  • P. Shiu
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Abstract

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.~Erd\H os, who made a conjecture on such distributions. We prove his conjecture by establishing a theorem on the ordering of residues.
Keywords: Euler's function, totatives Euler's function, totatives
MSC Classifications: 11A05, 11A07, 11A25 show english descriptions Multiplicative structure; Euclidean algorithm; greatest common divisors
Congruences; primitive roots; residue systems
Arithmetic functions; related numbers; inversion formulas
11A05 - Multiplicative structure; Euclidean algorithm; greatest common divisors
11A07 - Congruences; primitive roots; residue systems
11A25 - Arithmetic functions; related numbers; inversion formulas
 

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