p-adic numbers and Diophantine equations

Université de Bordeaux, Fall 2013, lectures by Yuri Bilu, TeXed by Alexey Beshenov.

The notes cover three different results:

• Hasse–Minkowski theorem (local-global principle for quadratic forms),

• Skolem–Mahler–Lech theorem about linear recurrences,

• Sprindžuk’s irreducibility theorem.

For any comments and suggestions, write to cadadr@gmail.com.