## Number Theory Seminar

### Wednesday, March 21st, 2018

**Time:** 2:15 p.m. **Place:** Jeffery Hall 319

**Speaker:** François Séguin (Queen's University)

**Title:** Frequency of primes dividing *n* and $\Phi_n$.

**Abstract:** ** ** In a previous talk, we have seen that at most one prime *P _{n}*, can divide both an integer

*n*and the nth cyclotomic polynomial evaluated at some integer

*a*. During this talk, we will use methods in Dirichlet series to investigate how often

*P*actually divides the nth cyclotomic polynomial $\Phi_n$.

_{n}