IMO 1978 LL VIE47

Origin: VIE

Problem

Given the expression Pn(x) = 1 2n  x + x2 −1 n +  x − x2 −1 n , prove: (a) Pn(x) satisfies the identity Pn(x) −xPn−1(x) + 1 4Pn−2(x) \equiv0. (b) Pn(x) is a polynomial in x of degree n.