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September 2015 On the diophantine equation $ax^{3} + by + c = xyz$
Sivanarayanapandian Subburam, Ravindrananathan Thangadurai
Funct. Approx. Comment. Math. 53(1): 167-175 (September 2015). DOI: 10.7169/facm/2015.53.1.9

Abstract

Consider the diophantine equation $ax^{3} + by + c = xyz$, where $a, b$ and $c$ are positive integers such that $\gcd(a, c) = 1$ and $c$ is square-free. Let $(x, y, z)$ be a positive integral solution of the equation. In this paper, we shall give an upper bound for $x$,$y$ and $z$ in terms of the given inputs $a$, $b$ and $c$. Also, we apply our results to investigate the divisors of the elements of the sequence $\{an^{3} + c\}$ in residue classes.

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Sivanarayanapandian Subburam. Ravindrananathan Thangadurai. "On the diophantine equation $ax^{3} + by + c = xyz$." Funct. Approx. Comment. Math. 53 (1) 167 - 175, September 2015. https://doi.org/10.7169/facm/2015.53.1.9

Information

Published: September 2015
First available in Project Euclid: 28 September 2015

zbMATH: 1374.11052
MathSciNet: MR3402776
Digital Object Identifier: 10.7169/facm/2015.53.1.9

Subjects:
Primary: 11D25
Secondary: 11D45

Rights: Copyright © 2015 Adam Mickiewicz University

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Vol.53 • No. 1 • September 2015
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