Question 7
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.
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.