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VJIMC 2015 Category I, Problem 3

Source: VJIMC2015

August 10, 2015
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Problem Statement

Problem 3 Let P(x)=x2015−2x2014+1 P(x) = x^{2015} -2x^{2014}+1 and Q(x)=x2015−2x2014−1 Q(x) = x^{2015} -2x^{2014}-1. Determine for each of the polynomials PP and QQ whether it is a divisor of some nonzero polynomial c0+c1x+…+cnxnc_0 + c_{1}x +\ldots + c_{n}x^n n whose coefficients cic_i are all in the set {−1,1} \{ -1, 1\}.
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