Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-28T07:35:50.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Almost Squares in Arithmetic Progression

Published online by Cambridge University Press:  04 December 2007

N. Saradha  and
T. N. Shorey
N. Saradha
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India. e-mail: saradha@math.tifr.res.in
T. N. Shorey
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India. e-mail: shorey@math.tifr.res.in
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is proved that a product of four or more terms of positive integers in arithmetic progression with common difference a prime power is never a square. More general results are given which completely solve (1.1) with gcd(n, d)=1, k≥3 and 1<d≤104.

Keywords

arithmetic progressionscongruencesdiophantine equationselliptic equationsLegendre symbolsquarefree integers
Type
Research Article
Information
Compositio Mathematica , Volume 138 , Issue 1 , August 2003 , pp. 73 - 111
Copyright
© 2003 Kluwer Academic Publishers