The minimum modulus problem for covering systems - Bob Hough

Analysis Seminar
Topic: The minimum modulus problem for covering systems
Speaker: Bob Hough
Affiliation: Member, School of Mathematics
Date: Wednesday, May 4

A distinct covering system of congruences is a finite collection of arithmetic progressions to distinct moduli aimodmi, whose union is the integers. Answering a question of Erdős, I have shown that the least modulus m1of a distinct covering system of congruences is at most. I will describe aspects of the proof, which involves the theory of smooth numbers and a relative form of the Lovász local lemma.