Divisibility of polynomials and degeneracy of integral points

Abstract We prove several statements about arithmetic hyperbolicity of certain blow-up varieties. As a corollary we obtain multiple examples simply connected quasi-projective varieties that are pseudo-arithmetically hyperbolic. This generalizes results Corvaja and Zannier obtained in dimension 2 to arbitrary dimension. The key input is an application the Ru–Vojta’s strategy. also analogue for function fields Nevanlinna theory with goal apply them future paper context Campana’s conjectures.