Number Theory Seminar: Paul Pollack

Abstract:

Let s(n) denote the sum of the proper divisors of n, so, e.g., s(4)=1+2=3. A natural number n is called *perfect* if s(n)=n and *amicable* if s(n) =/= n but s(s(n))=n. For example, 6 is a perfect number, and 220 is an amicable number. Questions about perfect and amicable numbers constitute some of the oldest unsolved problems in mathematics. I will talk about old and new theorems concerning these numbers and their generalizations. Some of this is joint work with Mits Kobayashi (Cal Poly Pomona), Florian Luca (Universidad Nacional Autónoma de México), and Carl Pomerance (Dartmouth College).