Proceedings of the Steklov Institute of Mathematics

, Volume 299, Issue 1, pp 132–142 | Cite as

On a Diophantine Inequality with Reciprocals

Article

Abstract

A sharpened lower bound is obtained for the number of solutions to an inequality of the form α ≤ {(an̅ + bn)/q} < β, 1 ≤ nN, where q is a sufficiently large prime number, a and b are integers with (ab, q) = 1, nn̅ ≡ 1 (mod q), and 0 ≤ α < β ≤ 1. The length N of the range of the variable n is of order qε, where ε > 0 is an arbitrarily small fixed number.

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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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