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DISTANCE BETWEEN ARITHMETIC PROGRESSIONS AND PERFECT SQUARES

Part of: Sequences and sets Diophantine equations Exponential sums and character sums Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  17 November 2010

Tsz Ho Chan
Tsz Ho Chan*
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A. (email: tchan@memphis.edu)

Abstract

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In this paper, we study how close the terms of a finite arithmetic progression can get to a perfect square. The answer depends on the initial term, the common difference and the number of terms in the arithmetic progression.

MSC classification

Secondary: 11J25: Diophantine inequalities 11D75: Diophantine inequalities 11B83: Special sequences and polynomials 11L05: Gauss and Kloosterman sums; generalizations

Information

Type
Research Article
Information
Mathematika , Volume 57 , Issue 1 , January 2011 , pp. 41 - 49
Copyright
Copyright © University College London 2011

References

[1]Chan, T. H., Finding almost squares. Acta Arith. 121(3) (2006), 221–232.CrossRefGoogle Scholar
[2]Friedlander, J. B. and Iwaniec, H., On the distribution of the sequence n 2θ (mod 1). Canad. J. Math. 39 (1987), 338–344.CrossRefGoogle Scholar
[3]Huxley, M. N., The integer points close to a curve. II. In Analytic Number Theory, Vol. 2 (Allerton Park, IL, 1995) (Progress in Mathematics 139), Birkhäuser Boston (Boston, MA, 1996), 487–516.Google Scholar