2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163318We prove that the sumset or the productset of any finite set of real numbers, $A,$ is at least $|A|^{4/3-ε},$ improving earlier bounds. Our main tool is a new upper bound on the multiplicative energy, $E(A,A).$Combinatorics68R05; 11B75text