2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132410Let $F$ be a non-zero polynomial with integer coefficients in $N$ variables of degree $M$. We prove the existence of an integral point of small height at which $F$ does not vanish. Our basic bound depends on $N$ and $M$ only. We separately investigate the case when $F$ is decomposable into a product of linear forms, and provide a more sophisticated bound. We also relate this problem to a certain extension of Siegel's Lemma as well as to Faltings' version of it. Finally we exhibit an application of our results to a discrete version of the Tarski plank problem.16 pages, revised version, to appear in Monatshefte für MathematikNumber Theory11C08; 11H06; 11D04; 11H46text