IMO 1986 LL FIN19

Let f : [0, 1] o[0, 1] satisfy f(0) = 0, f(1) = 1 and

imolonglistmathematicsolympiad

IMO 1986 LL FIN19

Origin: FIN

Problem

Let f : [0, 1] \to[0, 1] satisfy f(0) = 0, f(1) = 1 and f(x + y) −f(x) = f(x) −f(x −y) for all x, y \geq0 with x −y, x + y \in[0, 1]. Prove that f(x) = x for all x \in[0, 1].