Extreme Covering Systems of the Integers

2019/05/17 by Dalton, Jack, Trifonov, Ognian
#11A07 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1905.07386

Abstract

It is proved that if the least modulus of a distinct covering system is 4, its largest modulus is at least 60; also if the least modulus is 3, the LCM of the moduli is at least 120; finally, if the least modulus is 4, the LCM of the moduli is at least 360. The constants 60, 120, and 360 can not be replaced by larger constants.

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