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A GENERALIZATION OF THE RAMANUJAN–NAGELL EQUATION

Part of: Diophantine equations

Published online by Cambridge University Press:  22 August 2018

TOMOHIRO YAMADA Open the ORCID record for TOMOHIRO YAMADA [Opens in a new window]
TOMOHIRO YAMADA*
Affiliation:
Center for Japanese Language and Culture, Osaka University, 8-1-1, Aomatanihigashi, Minoo, Osaka 562-8558, Japan e-mail: tyamada1093@gmail.com
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Abstract

We shall show that, for any positive integer D > 0 and any primes p1, p2, the diophantine equation x2 + D = 2sp1kp2l has at most 63 integer solutions (x, k, l, s) with x, k, l ≥ 0 and s ∈ {0, 2}.

MSC classification

Primary: 11D61: Exponential equations
Secondary: 11D45: Counting solutions of Diophantine equations
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 3 , September 2019 , pp. 535 - 544
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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