MathDB

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

\dotsc

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} +\dotsb +a_j = P(k)

Problem Statement