Bounds for the size of sets with the property D(n)
Number Theory
2021-08-30 v2
Abstract
Let n be a nonzero integer and a_1 < a_2 < ... <a_m positive integers such that a_i*a_j + n is a perfect square for all 1 <= i < j <= m. It is known that m <= 5 for n = 1. In this paper we prove that m <= 31 for |n| <= 400 and m < 15.476 log|n| for |n| > 400.
Cite
@article{arxiv.math/0304242,
title = {Bounds for the size of sets with the property D(n)},
author = {Andrej Dujella},
journal= {arXiv preprint arXiv:math/0304242},
year = {2021}
}
Comments
9 pages. Revised - removed a gap in the proof of Proposition 1; to appear in Glasnik Matematicki