2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116525We prove, using combinatorics and Kloosterman sum technology that if $A \subset {\Bbb F}_q$, a finite field with $q$ elements, and $q^{1/2} \lesssim |A| \lesssim q^{7/10}$, then $\max \{|A+A|, |A \cdot A|\} \gtrsim \frac{{|A|}^{3/2}}{q^{1/4}$.CombinatoricsClassical Analysis and ODEs52C, 11L, 11Ctext