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Mathematics of Computation

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Integer points on the curve $ Y^{2}=X^{3}\pm p^{k}X$

Author: Konstantinos A. Draziotis
Journal: Math. Comp. 75 (2006), 1493-1505
MSC (2000): Primary 11D25, 11G05
Published electronically: April 6, 2006
MathSciNet review: 2219040
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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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Additional Information

Konstantinos A. Draziotis
Affiliation: 42 G. Passalidi St., Thessaloniki 54453, Greece

Keywords: Elliptic curve, 2-torsion point, unramified morphism, Pell equation.
Received by editor(s): December 2, 2003
Received by editor(s) in revised form: July 29, 2005
Published electronically: April 6, 2006
Additional Notes: The research of this author was supported by the Hellenic State Scholarships Foundation-I.K.Y
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.