## Number Theory - Riley Becker

### Wednesday, May 16th, 2018

**Time:** 2:30-3:20p.m. **Place:** Jeffery Hall 422

**Speaker:** Riley Becker

**Title:** The Size of Sets with the Property D(n).

**Abstract:** Let $n$ be a nonzero integer, and suppose $A$ is a set of distinct positive integers for which $ab+n$ is a perfect square for each pair of distinct $a$ and $b$ in $A$. Using a discussion of Andrej Dujella, we will find an upper bound on the size of such a set.