Asif Zaman, Fri Jan 11, 5:00 – 6:30 BA6183
Title: The multiplication table problem
The $N$ by $N$ multiplication table is formed by multiplying two integers from 1 to $N$. The numbers in the table are between 1 and $N^2$ but how many distinct numbers are in this table? By mixing ideas from probability and number theory, Erdös proved that very few numbers up to $N^2$ appear. I’ll describe the remarkably elegant proof and explore related probabilistic ideas when studying the anatomy of integers.