olymmath

CMO 2018 Problem 4

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  • Answer

Find all polynomials p(x)p(x) with real coefficients that have the following property: There exists a polynomial q(x)q(x) with real coefficients such that

p(1)+p(2)+p(3)+⋯+p(n)=p(n)q(n)p(1)+p(2)+p(3)+\cdots+p(n)=p(n) q(n)

for all positive integers nn.

Dataset text NuminaMath olympiads. Quoted with source.

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p(x)=c(x+r-1)(x+r-2) \cdots(x+r-d)

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