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

Source: Own. Malaysian SST 2023 P7

August 27, 2023
number theory

Problem Statement

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
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