3 papers
math.NT2026
Covering systems where the prime divisors of all moduli are only , , or
Joshua Harrington, Jonah Klein, Joshua Lowrance +1
We try to find all quadruples of positive integers with such that there exists a distinct covering system with minimum modulus and least common mu…
math.NT2025
On a conjecture of Krukenberg and a problem of Dalton and Trifonov
Jonah Klein
We prove that if the smallest modulus of a covering system with distinct moduli is , then the largest modulus is at least 108. We also prove that if the smallest modulus of a co…
math.NT2022
On the -th smallest modulus of a covering system with distinct moduli
Jonah Klein, Dimitris Koukoulopoulos, Simon Lemieux
Covering systems were introduced by Erdős in 1950. In the same article where he introduced them, he asked if the minimum modulus of a covering system with distinct moduli is bounde…