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IMO Shortlist 2013, Algebra 6

Source: IMO Shortlist 2013, Algebra 6

July 9, 2014
algebrapolynomialIMO Shortlist

Problem Statement

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) (x^3 - mx^2 +1 ) P(x+1) + (x^3+mx^2+1) P(x-1) =2(x^3 - mx +1 ) P(x) for all real number xx.
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