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arXiv · 1311.7077

Mordell's equation : a classical approach

Michael A. Bennett·Amir Ghadermarzi
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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.

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Michael A. Bennett, Amir Ghadermarzi. 2013-11-27. Mordell's equation : a classical approach. https://doi.org/10.1112/s1461157015000182

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