MathDB
Sum of certain images of P is still an image

Source: Own. Malaysian IMO TST 2024 P2

April 21, 2024
algebra

Problem Statement

Let kk be a positive integer. Find all collection of integers (a1,a2,⋯ ,ak)(a_1, a_2,\cdots, a_k) such that there exist a non-linear polynomial PP with integer coefficients, so that for all positive integers nn there exist a positive integer mm satisfying: P(n+a1)+P(n+a2)+...+P(n+ak)=P(m)P(n+a_1)+P(n+a_2)+...+P(n+a_k)=P(m)
Proposed by Ivan Chan Kai Chin
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