2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101110We give a sharpened form of Siegel Lemma's w. r. t. the maximum norm. This implies a new lower bound on the greatest element of a sum-distinct set of positive integers (Erdös-Moser problem). The main tools are Minkowski's theorem on successive minima and the Busemann theorem from convex geometry.10 pages, corrected typosNumber TheoryCombinatorics11H06; 11P70text