Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11D25, 11G05

Retrieve articles in all journals with MSC (2000): 11D25, 11G05

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.