MathNet 2024-part-03 — 168 problems (EN–VI) Question 8

Let $P(x) \in \mathbb{Q}[x]$ be a polynomial with rational coefficients and degree $d \ge 2$. Prove there is no infinite sequence $a_0, a_1, \dots$ of rational numbers such that $P(a_i) = a_{i-1} + i$ for all $i \ge 1$.