Speaker
Ingrid Vukusic
Description
Let $1< a < b < c$ be multiplicatively dependent integers (i.e., there exist nontrivial integer exponents $x, y, z$, such that $a^x b^y c^z = 1$). Is it possible that $a+1, b+1, c+1$ are multiplicatively dependent as well? It turns out that this is easy to answer. We will discuss related, more difficult questions, which will lead to Diophantine equations. We will solve some of them using lower bounds for linear forms in logarithms. Joint work with Volker Ziegler and work in progress.
