An upper bound for the minimum modulus in a covering system with squarefree moduli

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2025-01-18 DOI:10.1007/s10474-024-01496-x

M. Cummings, M. Filaseta, O. Trifonov

引用次数: 0

Abstract

Based on work of P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe and M. Tiba [5], we show that if a covering system has distinct squarefree moduli, then the minimum modulus is at most 118. We also show that in general the \(k\)-th smallest modulus in a covering system with distinct moduli (provided it is required for the covering) is bounded by an absolute constant.

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具有无平方模的覆盖系统最小模的上界

基于P. Balister， B. Bollobás， R. Morris， J. Sahasrabudhe和M. Tiba[5]的工作，我们证明了如果覆盖系统具有不同的无平方模量，则最小模量最多为118。我们还表明，在具有不同模的覆盖系统中（如果覆盖需要它），通常\(k\) -最小模是由一个绝对常数限定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.