Problem

Source: China Mathematical Olympiad 1992 problem1

Tags: inequalities, triangle inequality, algebra unsolved, algebra



Let equation xn+an1xn1+an2xn2++a1x+a0=0 with real coefficients satisfy 0<a0a1a2an11. Suppose that λ (|λ|>1) is a complex root of the equation, prove that λn+1=1.