Integer points on the curve 𝑌²=𝑋³±𝑝^{𝑘}𝑋

Draziotis, Konstantinos

doi:10.1090/S0025-5718-06-01852-7

Integer points on the curve $Y^{2}=X^{3}\pm p^{k}X$
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by Konstantinos A. Draziotis;

Math. Comp. 75 (2006), 1493-1505

DOI: https://doi.org/10.1090/S0025-5718-06-01852-7

Published electronically: April 6, 2006

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Abstract:

We completely solve diophantine equations of the form $Y^{2}=X^{3}\pm p^{k}X,$ where $k$ is a positive integer, using a reduction to some quartic elliptic equations, which can be solved with well known methods.

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