Investigations on some exponential congruences
dc.contributor.author | Bose, Arnab | |
dc.contributor.author | University of Lethbridge. Faculty of Arts and Science | |
dc.contributor.supervisor | Akbary-Majdabadno, Amir | |
dc.date.accessioned | 2016-08-05T17:21:14Z | |
dc.date.available | 2016-08-05T17:21:14Z | |
dc.date.issued | 2016 | |
dc.degree.level | Masters | en_US |
dc.description.abstract | Selfridge asked for what positive integers a and b with a > b, does 2a — 2b divide na — nb for all n e N. The problem was solved by various people who showed that the above problem is true only for (a, b) e S, where S = {(2,1), (3,1), (4,2), (5,1), (5,3), (6,2), (7,3), (8,2), (8,4), (9,3), (14,2), (15,3), (16,4)}. In this thesis, we prove two generalizations of the above problem. Theorem. For a fixed positive integer m, na — nb = 0 (mod ma — mb) has a solution in (a, b) e N2 with a > b, for all integers n > m if and only ifm = 2 and (a, b) e S, where S is as given above. Zaharescu and Vajaitu considered a generalization of Selfridge’s problem in algebraic number fields. Our second result makes their theorem explicit and provides explicit bounds for the solutions. Next, we give a conditional resolution to a problem proposed by Ruderman which is related to Selfridge’s problem and also investigate some generalizations. Lastly, we use a particular case of the Schmidt Subspace Theorem and generalize a result proved by Bugeaud, Corvaja and Zannier [2]. | en_US |
dc.embargo | No | en_US |
dc.identifier.uri | https://hdl.handle.net/10133/4567 | |
dc.language.iso | en_CA | en_US |
dc.proquest.subject | 0405 | en_US |
dc.proquestyes | Yes | en_US |
dc.publisher | Lethbridge, Alta : University of Lethbridge, Dept. of Mathematics and Computer Science | en_US |
dc.publisher.department | Department of Mathematics and Computer Science | en_US |
dc.publisher.faculty | Arts and Science | en_US |
dc.relation.ispartofseries | Thesis (University of Lethbridge. Faculty of Arts and Science) | en_US |
dc.subject | mathematics | en_US |
dc.subject | number theory | en_US |
dc.subject | Ruderman's problem | en_US |
dc.subject | Schmidt Subspace Theorem | en_US |
dc.subject | Selfridge's problem | en_US |
dc.title | Investigations on some exponential congruences | en_US |
dc.type | Thesis | en_US |