2

Part of 1982 Canada National Olympiad

Problems(1)

On the roots of x^3 = x^2 + x + 1 - [Canada MO 1982 - P2]

Source:

a

b

c

are the roots of the equation

x^3 - x^2 - x - 1 = 0

, (i) show that

a

b

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}