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Extreme Covering Systems of the Integers (1905.07386v2)
Published 17 May 2019 in math.NT
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.
