IMO 1976 LL VIE50

Find a function f(x) defined for all real values of x such that

IMO 1976 LL VIE50

Origin: VIE

Problem

Find a function f(x) defined for all real values of x such that for all x, f(x + 2) −f(x) = x2 + 2x + 4, and if x \in[0, 2), then f(x) = x2.