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2014 The method of infinite ascent applied on $2^pA^6+B^3 = C^2$
Susil Kumar Jena
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Tbilisi Math. J. 7(1): 31-36 (2014). DOI: 10.2478/tmj-2014-0003

Abstract

In this paper, we prove that for any positive integer $p$, when $p \equiv 1\pmod{6}$ or, $p \equiv 3 \pmod{6}$, the Diophantine equation: $2^p A^6 + B^3 = C^2$ has infinitely many co-prime integral solutions $A$, $B$, $C$. When $p=0$, this equation has only four integral solutions with $(A, B, C)= (\pm1,2,\pm3)$. For other integer values of $p$, the problem is open.

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Susil Kumar Jena. "The method of infinite ascent applied on $2^pA^6+B^3 = C^2$." Tbilisi Math. J. 7 (1) 31 - 36, 2014. https://doi.org/10.2478/tmj-2014-0003

Information

Received: 24 March 2013; Accepted: 15 May 2014; Published: 2014
First available in Project Euclid: 12 June 2018

zbMATH: 1306.11026
MathSciNet: MR3313042
Digital Object Identifier: 10.2478/tmj-2014-0003

Subjects:
Primary: 11D41
Secondary: 11D72

Rights: Copyright © 2014 Tbilisi Centre for Mathematical Sciences

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Vol.7 • No. 1 • 2014
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