VMO 2001 Problem 3

For real a, b define the sequence $x_0$, $x_1$, $x_2$, ... by $x_0$ = a, $x_{n+1}$ = $x_n$ + b sin $x_n$. If b = 1, show that the sequence converges to a finite limit for all a. If b > 2, show that the sequence diverges for some a.