Mordell’s equation: a classical approach

Michael A. Bennett, Amir Ghadermarzi

Type: Article

Publication Date: 2015-01-01

Citations: 25

DOI: https://doi.org/10.1112/s1461157015000182

Abstract

We solve the Diophantine equation $Y^2=X^3+k$ for all nonzero integers $k$ with $|k| \leq 10^7$. Our approach uses a classical connection between these equations and cubic Thue equations. The latter can be treated algorithmically via lower bounds for linear forms in logarithms in conjunction with lattice-basis reduction.

Locations

LMS Journal of Computation and Mathematics - View - PDF
arXiv (Cornell University) - View - PDF
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