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KöMaL problem A, 2021

Algebra Difficulty 7.0 National Olympiad, round 2 Find the answer Hungary

For which values of positive integer mm is it possible to find polynomials p,q∈C[x]p,q\in \mathbb{C}[x] with degrees at least two such that x(x+1)⋯(x+m−1)=p(q(x))x(x+1)\cdots(x+m-1) =p\big(q(x)\big)?

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