MathDB

Impossible Infinite Sequence

Source: India IMOTC 2024 Day 1 Problem 3

May 31, 2024

number theory

Problem Statement

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, \ldots

of rational numbers such that

P(a_i)=a_{i-1}+i

for all

i\ge 1

.
Proposed by Pranjal Srivastava and Rohan Goyal