Persistent Link:
http://hdl.handle.net/10150/185436
Title:
Integral solutions in arithmetic progression for elliptic curves.
Author:
Lee, June-Bok.
Issue Date:
1991
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Integral solutions to y² = X³ + k, where either the x's or the y's, or both, are in arithmetic progression are studied. When both the x's and the y's are in arithmetic progression, then this situation is completely solved. One set of solutions where the y's formed an arithmetic progression of length 4 have already been constructed. In this dissertation, we construct infinitely many set of solutions where there are 4 x's in arithmetic progression and we also disprove Mohanty's Conjecture[8] by constructing infinitely many set of solutions where there are 4, 5 and 6 y's in arithmetic progression.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic; Curves, Elliptic; Arithmetic.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Yelez, William Y.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleIntegral solutions in arithmetic progression for elliptic curves.en_US
dc.creatorLee, June-Bok.en_US
dc.contributor.authorLee, June-Bok.en_US
dc.date.issued1991en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIntegral solutions to y² = X³ + k, where either the x's or the y's, or both, are in arithmetic progression are studied. When both the x's and the y's are in arithmetic progression, then this situation is completely solved. One set of solutions where the y's formed an arithmetic progression of length 4 have already been constructed. In this dissertation, we construct infinitely many set of solutions where there are 4 x's in arithmetic progression and we also disprove Mohanty's Conjecture[8] by constructing infinitely many set of solutions where there are 4, 5 and 6 y's in arithmetic progression.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academicen_US
dc.subjectCurves, Ellipticen_US
dc.subjectArithmetic.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorYelez, William Y.en_US
dc.contributor.committeememberKamienny, Sheldonen_US
dc.contributor.committeememberMadden, Danen_US
dc.identifier.proquest9123487en_US
dc.identifier.oclc709782516en_US
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