Question 63
Find all polynomials $P$ with real coefficients such that the following equation holds for all $x \in \mathbb{R}$:
$$
(x-2) P(x+2)+(x+2) P(x-2)=2 x P(x)
$$
$$
(x-2) P(x+2)+(x+2) P(x-2)=2 x P(x)
$$
MathNet 2016-part-06 — 184 problems (EN–VI) Question 63
Math Olympiad Vault · MathNet 2016-part-06 — 184 problems (EN–VI)