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ISL 2013 A6

  • Answer

Let m≠0m \neq 0 be an integer. Find all polynomials P(x)P(x) with real coefficients such that (x3−mx2+1)P(x+1)+(x3+mx2+1)P(x−1)=2(x3−mx+1)P(x)\left(x^{3}-m x^{2}+1\right) P(x+1)+\left(x^{3}+m x^{2}+1\right) P(x-1)=2\left(x^{3}-m x+1\right) P(x) for all real numbers xx. (Serbia)

Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.

Official text: IMO 2013 Shortlist booklet, page 3.

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P(x)=t x

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

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