The Paley graph conjecture and Diophantine m-tuples
Date
2020
Authors
Editor(s)
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
BUIR Usage Stats
3
views
views
14
downloads
downloads
Citation Stats
Series
Abstract
A Diophantine m-tuple with property D(n), where n is a nonzero integer, is a set of m positive integers {a1, ..., am} such that aiaj + n is a perfect square for all 1 i < j m. It is known that Mn = sup{|S| : S is a D(n) m-tuple} exists and is O(log |n|). In this paper, we show that the Paley graph conjecture implies that the upper bound can be improved to (log |n|), for any > 0.
Source Title
Journal of Combinatorial Theory, Series A
Publisher
Elsevier
Course
Other identifiers
Book Title
Degree Discipline
Degree Level
Degree Name
Citation
Permalink
Published Version (Please cite this version)
Collections
Language
English