### Covering systems of congruences

- Series
- School of Mathematics Colloquium
- Time
- Thursday, February 22, 2018 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Robert Hough – Stony Brook University

A distinct covering system of congruences is a finite collection of arithmetic progressions $$a_i \bmod m_i, \qquad 1 < m_1 < m_2 < \cdots < m_k.$$Erdős asked whether the least modulus of a distinct covering system of congruences can be arbitrarily large. I will discuss my proof that minimum modulus is at most $10^{16}$, and recent joint work with Pace Nielsen, in which it is proven that every distinct covering system of congruences has a modulus divisible by either 2 or 3.