MORDELL’S EQUATION: A CLASSICAL APPROACH
Michael A. Bennett, Amir Ghadermarzi · 2016
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.