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2018 Ramanujan-Nagell cubics
Mark Bauer, Michael A. Bennett
Rocky Mountain J. Math. 48(2): 385-412 (2018). DOI: 10.1216/RMJ-2018-48-2-385

Abstract

A well-known result of Beukers on the generalized Ramanujan-Nagell equation has, at its heart, a lower bound on the quantity $|x^2-2^n|$. In this paper, we derive an inequality of the shape $|x^3-2^n| \geq x^{4/3}$, valid provided $x^3 \neq 2^n$ and $(x,n) \neq (5,7)$, and then discuss its implications for a variety of Diophantine problems.

Citation

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Mark Bauer. Michael A. Bennett. "Ramanujan-Nagell cubics." Rocky Mountain J. Math. 48 (2) 385 - 412, 2018. https://doi.org/10.1216/RMJ-2018-48-2-385

Information

Published: 2018
First available in Project Euclid: 4 June 2018

zbMATH: 06883472
MathSciNet: MR3809151
Digital Object Identifier: 10.1216/RMJ-2018-48-2-385

Subjects:
Primary: 11A63
Secondary: 11D61, 11J68

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 2 • 2018
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