Artyom Olegovich Radomskii

Long intervals of consecutive composite values of polynomials

Let $f\in\mathbb Q[t]$ be an irreducible polynomial of positive degree with positive leading coefficient, taking integer values at every integer. We prove that there is a constant $c_f>0$ such that, for every sufficiently large real $X$, the interval $(X/2,X]$ contains at least $...