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On polynomial

Source: Chinese TST 2009 3rd quiz P3

March 22, 2009
algebrapolynomialinductionmodular arithmeticbinomial coefficientsalgebra proposed

Problem Statement

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