Question 97
Let $n$ be an integer, $n \ge 2$, and let $\alpha_1, \alpha_2, \dots, \alpha_n$ be non-zero complex numbers such that $|\alpha_i| \lt 1$ for $i = 1, \dots, n-1$, and the coefficients of the polynomial $\prod_{i=1}^n (X - \alpha_i)$ are all integral. Show that, if $\alpha_i, \alpha_j, \alpha_k$ form a geometric progression, then $i = j = k$.