ACAC Seminar Abstract

ACAC Seminar Abstract

ACAC Seminars

ACAC Seminar Abstract

Exponential Diophantine equations

Speaker: Yann Bugeaud
Date, Time: Fri, 09 Mar 2012 13:00

The theory of linear forms in the logarithms of algebraic numbers, developed by Alan Baker, provides us with explicit upper bounds for the size of the solutions of certain families of Diophantine equations. Unfortunately, these upper bounds are huge, and we cannot hope to list all the solutions by brutal enumeration.

However, many important progress have been accomplished during the last ten years and, by combining various methods, it is now possible to completely solve certain famous exponential Diophantine equations. For instance, jointly with Mignotte and Siksek, we have proved recently that 1, 8 and 144 are the only perfect powers in the Fibonacci sequence.

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