2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141931We prove that for any real polynomial $f(x) \in\mathbb{R} [x]$ the set $$ \{α\in \mathbb{R}: \liminf_{n\to \infty} n\log n ||αf(n)|| >0\} $$ has positive Hausdorff dimension. Here $||ξ||$ means the distance from $ξ$ to the nearest integer. Our result is based on an original method due to Y. Peres and W. Schlag.8 pagesNumber Theory11J54text