**SMS scnews item created by Boris Lishak at Tue 29 Jan 2019 1047**

Type: Seminar

Modified: Tue 29 Jan 2019 1326; Wed 30 Jan 2019 1453

Distribution: World

**Calendar1: 31 Jan 2019 1100-1200**

**CalLoc1: Carslaw 159**

CalTitle1: Bugeaud -- Exponential Diophantine equations

Auth: borisl@144.138.19.29 (blis3801) in SMS-WASM

### Geometry and Topology Seminar

# Exponential Diophantine equations

### Yann Bugeaud (Strasbourg)

Please join us for lunch after the talk.
**Abstract:**

After a short survey of results obtained by Thue and Siegel about one century ago, we
explain how the theory of linear forms in the logarithms of algebraic numbers,
developed by Alan Baker in the 60s, applies to Diophantine equations and provides us with
explicit upper bounds for the size of the integer solutions of certain families of
equations. Unfortunately, these upper bounds are huge, and we cannot hope to
list all the integer solutions by brutal enumeration. However, many important progress
have been accomplished during the last twenty years and, by combining various
methods, it is now possible to completely solve some famous exponential Diophantine
equations. For instance, jointly with Mignotte and Siksek, we have
proved in 2006 that 1, 8 and 144 are the only perfect powers in the Fibonacci sequence.