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2019 Iberoamerican Mathematical Olympiad, P2

Source:

September 15, 2019
algebrapolynomialIbero-American

Problem Statement

Determine all polynomials P(x)P(x) with degree n≥1n\geq 1 and integer coefficients so that for every real number xx the following condition is satisfied P(x)=(x−P(0))(x−P(1))(x−P(2))⋯(x−P(n−1))P(x)=(x-P(0))(x-P(1))(x-P(2))\cdots (x-P(n-1))
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