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On Integers n Relatively Prime To ƒ(n)

Published online by Cambridge University Press:  20 November 2018

Joachim Lambek  and
Leo Moser
Joachim Lambek
Affiliation:
McGill University Research Institute, Canadian Mathematical Congress
Leo Moser
Affiliation:
University of Alberta Research Institute, Canadian Mathematical Congress
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1. Introduction. If m and n are two integers chosen at random, the probability that they are relatively prime (2, p. 267) is 6π-2. This result may still hold when m and n are functionally related. Thus, Watson (3) recently proved that for α irrational, the positive integers n for which (n, [αn]) = 1, have density 6π-2. A different proof of a slightly more general result was given by Estermann (1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 155 - 158
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Estermann, T., On the number of primitive lattice points in a parallelogram, Can. J. Math., 5 (1953), 456–459.Google Scholar
2. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (Oxford, 1938).Google Scholar
3. Watson, G. L., On integers n relatively prime to [αn], Can. J. Math., 5 (1953), 451–455.Google Scholar