具有性质 D(n) 的集合的大小的界
数论
2021-08-30 v2
摘要
设 n 为非零整数，a_1 < a_2 < ... < a_m 为正整数，使得对所有 1 <= i < j <= m，a_i*a_j + n 均为完全平方数。已知当 n = 1 时 m <= 5。本文中我们证明当 |n| <= 400 时 m <= 31，且当 |n| > 400 时 m < 15.476 log|n|。
引用
@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}
}
备注
9 pages. Revised - removed a gap in the proof of Proposition 1; to appear in Glasnik Matematicki