Diophantine equations and p-adic analysis

Research Horizons Seminar
Wednesday, November 14, 2012 - 12:05pm
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech, School of Math
I will discuss how one can solve certain concrete problems in number theory, for example the Diophantine equation 2x^2 + 1 = 3^m, using p-adic analysis. No previous knowledge of p-adic numbers will be assumed. If time permits, I will discuss how similar p-adic analytic methods can be used to prove the famous Skolem-Mahler-Lech theorem: If a_n is a sequence of complex numbers satisfying some finite-order linear recurrence, then for any complex number b there are only finitely many n for which a_n = b.