Persistent Link:
http://hdl.handle.net/10150/186902
Title:
THE DETERMINATION OF RAMANUJAN PAIRS.
Author:
BLECKSMITH, RICHARD FRED.
Issue Date:
1983
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:
We call two increasing sequences of positive integers {aᵢ}, {b(j)} a "Ramanujan Pair" if the following identity holds: (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI). The goal of this investigation is to determine all Ramanujan Pairs. Although this goal was not completely reached, we have determined all pairs for which the first term a₁ ≥ 5 and have proved that any Ramanujan Pair which begins with a₁ = m, where 1 ≤ m ≤ 4, aside from the known pairs, would have to branch off the first Euler identity with {aᵢ} = {i + m - 1}, {b(j)} = {j m}. A great deal of computing was done to discover the proofs given here. The search methods used and their programs are discussed in detail. Beyond these results, we have found all finite Ramanujan Pairs. Finally, modular Ramanujan Pairs (where the coefficients in the identity are reduced modulo n) are also examined.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics -- Data processing.; Functions -- Data processing.; Number theory.; Computer simulation.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleTHE DETERMINATION OF RAMANUJAN PAIRS.en_US
dc.creatorBLECKSMITH, RICHARD FRED.en_US
dc.contributor.authorBLECKSMITH, RICHARD FRED.en_US
dc.date.issued1983en_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.abstractWe call two increasing sequences of positive integers {aᵢ}, {b(j)} a "Ramanujan Pair" if the following identity holds: (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI). The goal of this investigation is to determine all Ramanujan Pairs. Although this goal was not completely reached, we have determined all pairs for which the first term a₁ ≥ 5 and have proved that any Ramanujan Pair which begins with a₁ = m, where 1 ≤ m ≤ 4, aside from the known pairs, would have to branch off the first Euler identity with {aᵢ} = {i + m - 1}, {b(j)} = {j m}. A great deal of computing was done to discover the proofs given here. The search methods used and their programs are discussed in detail. Beyond these results, we have found all finite Ramanujan Pairs. Finally, modular Ramanujan Pairs (where the coefficients in the identity are reduced modulo n) are also examined.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics -- Data processing.en_US
dc.subjectFunctions -- Data processing.en_US
dc.subjectNumber theory.en_US
dc.subjectComputer simulation.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.identifier.proquest8323736en_US
dc.identifier.oclc690027919en_US
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