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September 2008 Explicit estimates of solutions of some Diophantine equations
Robert Juricevic
Funct. Approx. Comment. Math. 38(2): 171-194 (September 2008). DOI: 10.7169/facm/1229696538

Abstract

Let $k$ be a fixed non-zero integer, and let $x$ and $y$ be integers such that $$y^2=x^3+k.$$ We show that $$\log \max\{|x|,|y|\}<\min_{(c,d)\in S} \{c|k|(\log |k|)^d\},$$ where $$S=\{(10^{181},4), (10^{23},5), (10^{19},6)\}.$$

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Robert Juricevic. "Explicit estimates of solutions of some Diophantine equations." Funct. Approx. Comment. Math. 38 (2) 171 - 194, September 2008. https://doi.org/10.7169/facm/1229696538

Information

Published: September 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1214.11038
MathSciNet: MR2492855
Digital Object Identifier: 10.7169/facm/1229696538

Subjects:
Primary: 11D25
Secondary: 11D99 , 11J86

Keywords: Hall's conjecture , linear forms in logarithms , Mordell equation

Rights: Copyright © 2008 Adam Mickiewicz University

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Vol.38 • No. 2 • September 2008
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