## Lethbridge Number Theory and Combinatorics Seminar: Ram Murty

- Date: 05/08/2015
- Time: 10:30

Lecturer(s):
Ram Murty,

*Queen's*
Location:

University of Lethbridge

Topic:

Consecutive Squarefull Numbers

Description:

A number $n$ is called squarefull if for every prime $p$ dividing $n$, we have $p^2$ also dividing $n$.

Erdos conjectured that the number of pairs of consecutive squarefull numbers $(n, n+1)$ with $n < N$ is at most $(log N)^A$ for some $A >0$.

This conjecture is still open. We will show that the abc conjecture implies this number is at most $N^e$ for any $e>0$. We will also discuss a related conjecture of Ankeny, Artin and Chowla on fundamental units of certain real quadratic fields and discuss its connection with the Erdos conjecture.

This is joint work with Kevser Aktas.

Other Information: