2019 OIM Problems/Problem 2

Problem

Find all polynomials $P(x)$ of degree $n \ge 1$ with integer coefficients such that for every real number $x$ it holds

\[P(x) = (x - P(0))(x - P(1))(x - P(2))\cdots(x - P(n - 1))\]

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions