MathDB
Interesting Polynomial

Source: Azerbaijan IMO TST 2016, D3 P2

May 26, 2018
algebrapolynomial

Problem Statement

A positive interger nn is called rising if its decimal representation akak−1⋯a0a_ka_{k-1}\cdots a_0 satisfies the condition ak≤ak−1≤⋯≤a0a_k\le a_{k-1}\le\cdots \le a_0. Polynomial PP with real coefficents is called interger-valued if for all integer numbers nn, P(n)P(n) takes interger values. P(n)P(n) is called rising-valued if for all rising numbers nn, P(n)P(n) takes integer values. Does it necessarily mean that, "every rising-valued PP is also interger-valued PP"?
Back to ProblemsView on AoPS