APMO 2020 P4

Discussion on Asian Pacific Mathematical Olympiad (APMO)
Soumitro_Shovon
Posts:5
Joined:Fri Aug 21, 2020 11:39 am
APMO 2020 P4

Unread post by Soumitro_Shovon » Thu Dec 03, 2020 9:23 pm

Let $\mathbb{Z}$ denote the set of all integers. Find all polynomials $P(x)$ with integer coefficients that satisfy the following property:

For any infinite sequence $a_1$, $a_2$, $\cdots$ of integers in which each integer in $\mathbb{Z}$ appears exactly once, there exist indices $i < j$ and an integer $k$ such that $a_i +a_{i+1} +\cdots +a_j = P(k)$.

Post Reply