CMO 1982 Problem 2

If $a$ , $b$ and $c$ are the roots of the equation $x^3 - x^2 - x - 1 = 0$ , (i) show that $a$ , $b$ and $c$ are distinct: (ii) show that $$\frac{a^{1982} - b^{1982}}{a - b} + \frac{b^{1982} - c^{1982}}{b - c} + \frac{c^{1982} - a^{1982}}{c - a}$$ is an integer.