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Diophantine approximation with square-free integers

  • Glyn Harman (a1)

In this paper we shall prove the following two results.

Theorem 1. Let ∊ > 0 and β a real number be given. Them, for almost all real a (in the sense of Lebesque measure), there are infinitely many pairs of square-free integers m, n such that

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[1] H. Davenport . Multiplicative Number Theory, 2nd ed. Revised by H. L. Montgomery . (Springer-Verlag, 1980).

[11] H. L. Montgomery . Topics in Multiplicative Number Theory. (Springer-Verlag, 1971).

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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