Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T17:12:42.646Z Has data issue: false hasContentIssue false
  • English
  • Français

DISTANCE BETWEEN ARITHMETIC PROGRESSIONS AND PERFECT SQUARES

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

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: [email protected])
Get access

Abstract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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