The Library
Differences between perfect powers : prime power gaps
Tools
Tools
Tools
Bennett, Michael A. and Siksek, Samir (2022) Differences between perfect powers : prime power gaps. Algebra & Number Theory, 376 . pp. 335-370. doi:10.1090/tran/8734 ISSN 1937-0652.
|
PDF
WRAP-Differences-between-perfect-powers-prime-power-gaps-22.pdf - Accepted Version - Requires a PDF viewer. Download (754Kb) | Preview |
Official URL: https://doi.org/10.1090/tran/8734
Abstract
We develop a variety of new techniques to treat Diophantine equations of the shape x2+D=yn, based upon bounds for linear forms in p-adic and complex logarithms, the modularity of Galois representations attached to Frey-Hellegouarch elliptic curves, and machinery from Diophantine approximation. We use these to explicitly determine the set of all coprime integers x and y, and n≥3, with the property that yn>x2 and x2−yn has no prime divisor exceeding 11.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Diophantine analysis, Fermat's last theorem, Galois theory | ||||||
| Journal or Publication Title: | Algebra & Number Theory | ||||||
| Publisher: | Mathematical Sciences Publishers | ||||||
| ISSN: | 1937-0652 | ||||||
| Official Date: | 24 October 2022 | ||||||
| Dates: |
|
||||||
| Volume: | 376 | ||||||
| Page Range: | pp. 335-370 | ||||||
| DOI: | 10.1090/tran/8734 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | First published in Algebra & Number Theory in Vol.376, 335-370. published by Mathematical Sciences Publishers,” © Copyright 2022 American Mathematical Society | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | © Copyright 2022 American Mathematical Society | ||||||
| Date of first compliant deposit: | 30 November 2022 | ||||||
| Date of first compliant Open Access: | 28 July 2023 | ||||||
| RIOXX Funder/Project Grant: |
|
||||||
| Related URLs: | |||||||
| Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
