t. In this paper, we study the set A = {p(n) + 2 n d mod 1 : n ≥ 1} ⊂ [0, 1], where p is a polynomial with at least one irrational coefficient on non-constant terms, d is any real number and, for a ∈ [0, ∞), a mod 1 is the fractional part of a. With the help of a method recently introduced by Wu, we show that the closure of A must have full Hausdorff dimension