The Erdős–Selfridge problem with square-free moduli

A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of covering systems with distinct moduli was initiated by Erdős in 1950, and over the following decades numerous problems were posed regarding their properties. One particularly notoriou...

Ամբողջական նկարագրություն

Մատենագիտական մանրամասներ
Հիմնական հեղինակներ: Balister, P, Bollobás, B, Morris, R, Sahasrabudhe, J, Tiba, M
Ձևաչափ: Journal article
Լեզու:English
Հրապարակվել է: Mathematical Sciences Publishers 2021
Նկարագրություն
Ամփոփում:A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of covering systems with distinct moduli was initiated by Erdős in 1950, and over the following decades numerous problems were posed regarding their properties. One particularly notorious question, due to Erdős, asks whether there exist covering systems whose moduli are distinct and all odd. We show that if in addition one assumes the moduli are square-free, then there must be an even modulus.