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Q(x) = (x + 1)P(x-1) -(x-1)P(x) is constant

Source: New Zealand NZMOC Camp Selection Problems 2016 p5

September 19, 2021
algebrapolynomial

Problem Statement

Find all polynomials P(x)P(x) with real coefficients such that the polynomial Q(x)=(x+1)P(x−1)−(x−1)P(x)Q(x) = (x + 1)P(x-1) -(x-1)P(x) is constant.
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