Combinatorial problems in finite fields and Sidon sets

Javier Cilleruelo

Published 2010-03-18, updated 2011-02-18Version 2

We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solubility of some equations and distribution of sequences in small intervals. We obtain classic and more recent results avoiding the use of exponential sums, the usual tool to deal with these problems.