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On Integers n Relatively Prime To ƒ(n)

  • Joachim Lambek (a1) and Leo Moser (a2)

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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).

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References

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1. Estermann, T., On the number of primitive lattice points in a parallelogram, Can. J. Math., 5 (1953), 456459.
2. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (Oxford, 1938).
3. Watson, G. L., On integers n relatively prime to [αn], Can. J. Math., 5 (1953), 451455.
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On Integers n Relatively Prime To ƒ(n)

  • Joachim Lambek (a1) and Leo Moser (a2)

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