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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
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Abstract

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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