2 problems

Let $\alpha_1,\dots,\alpha_k\in\mathbb{R}$, let $h\in\mathbb{Z}[x]$ be an intersective polynomial of degree $\ell$, and let $N\in\mathbb{N}$. Theorem B gives an integer…

Let $p_1,\ldots,p_r$ be integral polynomials in one variable. The natural conjecture that these polynomials are jointly intersective if every linear combination of them is intersec…