2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67103Let q be a prime, A be a subset of a finite field $F=\Bbb Z/q\Bbb Z$, $|A|<\sqrt{|F|}$. We prove the estimate $\max(|A+A|,|A\cdot A|)\ge c|A|^{1+ε}$ for some $ε>0$ and c>0. This extends the result of J. Bourgain, N. Katz, and T. Tao.Number Theory11B75,11T30text