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 $$S=\{(10^{181},4), (10^{23},5), (10^{19},6)\}.$$
Citation
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
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