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On Integers n Relatively Prime to [αn]

Published online by Cambridge University Press:  20 November 2018

G. L. Watson
G. L. Watson*
Affiliation:
University College, London
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The object of this paper is to consider a problem suggested by Dr. K. F. Roth, on the distribution of integers n that are relatively prime to the integral part of an, a being a fixed real number. He conjectured that the number of positive integers up to x with this property is asymptotic to (or in other words that they have the density ), for irrational a. I prove this and rather more in the following

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 451 - 455
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Vinogradov, I. M., Osnovy teorii čisel (Moscow and Leningrad, 1949).Google Scholar
2. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (Oxford, 1938).Google Scholar