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MathNet 2008-part-01 — 165 problems (EN–VI) Question 50

Math Olympiad Vault · MathNet 2008-part-01 — 165 problems (EN–VI)

Question 50

Determine all polynomials $p(x)$ with real coefficients such that
$$
p\left((x+1)^3\right) = (p(x)+1)^3
$$
and
$$
p(0) = 0
$$