Problem

Source: Chinese TST 2009 3rd quiz P3

Tags: algebra, polynomial, induction, modular arithmetic, binomial coefficients, algebra proposed



Let $ f(x)$ be a $ n -$degree polynomial all of whose coefficients are equal to $ \pm 1$, and having $ x = 1$ as its $ m$ multiple root. If $ m\ge 2^k (k\ge 2,k\in N)$, then $ n\ge 2^{k + 1} - 1.$