Lethbridge Number Theory and Combinatorics Seminar: Soroosh Yazdani

Let $S$ be a finite collection of prime numbers. We say a number is an $S$-unit if it is a product of powers of primes in $S$. For instance $-3/8$ is an example of a $\{2,3\}$-unit. Many interesting Diophantine equations are reduced to solving equations of the form \[ x+y=1 \] with $x$ and $y$ both being an $S$-unit. Using linear forms of logarithms, we can show that there only finitely many solutions to these $S$-unit equations. In this talk, I will explain an algorithm (due primarily to Smart and Wildanger) on how we can actually enumerate all these solutions.