This article is available for purchase or by subscription. See below.
Abstract
|
We examine certain representations of integers by prime powers. Specifically, we show that given
two primes
and
,
every integer has a bounded number of representations of the form
, with
,
,
and
nonnegative integers. Furthermore, we show that apart from finitely many integers
and integers within a short list of infinite families, no positive integer allows more
than one representation of this form.
|
PDF Access Denied
We have not been able to recognize your IP address
3.149.236.69
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 30.00:
Keywords
$S$-units, powers of primes, Diophantine equations, Catalan
conjecture
|
Mathematical Subject Classification
Primary: 11D85
|
Milestones
Received: 22 September 2021
Revised: 26 July 2022
Accepted: 3 September 2022
Published: 31 October 2023
Communicated by Bjorn Poonen
|
© 2023 MSP (Mathematical Sciences
Publishers). |
|