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Existence of a weird polynomial satisfying divisibility condition

Source: All-Russian MO Final stage 2023 10.3

April 23, 2023
number theory

Problem Statement

Given are positive integers a,ba, b satisfying a≥2ba \geq 2b. Does there exist a polynomial P(x)P(x) of degree at least 11 with coefficients from the set {0,1,2,…,b−1}\{0, 1, 2, \ldots, b-1 \} such that P(b)∣P(a)P(b) \mid P(a)?
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