2023 OIM Problems/Problem 6

Problem

Let $P$ be a polynomial of degree greater than or equal to 4 with integer coefficients. An integer $x$ is called $P$ -representable if there exist integers $a$ and $b$ such that $x = P(a) - P(b)$ . Prove that, if for all $N \ge 0$ , more than half of the integers in the set ${0, 1, \cdots, N}$ are $P$ -representable, then all even integers are $P$ -representable or all odd integers are $P$ -representable.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Page

Toolbox

Search

2023 OIM Problems/Problem 6

Problem

Solution

See also