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TOT 257 1990 Spring A S1 P(x) divisible by (x-1)^n

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June 8, 2024
algebrapolynomial

Problem Statement

Prove that for all natural nn there exists a polynomial P(x)P(x) divisible by (x−1)n(x-1)^n such that its degree is not greater than 2n2^n and each of its coefficients is equal to 11, 00 or −1-1.
(D. Fomin, Leningrad)
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