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Polynomial with coefficients -1 or 1

Source: Kvant Magazine No. 9 2019 M2575

March 14, 2023
algebrapolynomialKvant

Problem Statement

Let t∈(1,2)t\in (1,2). Show that there exists a polynomial P(x)=anxn+an−1xn−1+...+a1x+a0P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0 with the coefficients in {1,−1}\{1,-1\} such that ∣P(t)−2019∣⩽1.\left|P(t)-2019\right| \leqslant 1.
Proposed by N. Safaei (Iran)
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