MathDB

7

Part of 2023 Malaysian IMO Training Camp

Problems(1)

0, P(0), P(P(0)), ... eventually constant mod n

Source: Own. Malaysian SST 2023 P7

8/27/2023
Find all polynomials with integer coefficients PP such that for all positive integers nn, the sequence 0,P(0),P(P(0)),⋯0, P(0), P(P(0)), \cdots is eventually constant modulo nn.
Proposed by Ivan Chan Kai Chin
number theory