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Polynomial without negative integer roots has many positive integer roots

Source: 2020 China Southeast 10.3/11.3

August 7, 2020
algebrapolynomial

Problem Statement

Given a polynomial f(x)=x2020+∑i=02019cixif(x)=x^{2020}+\sum_{i=0}^{2019} c_ix^i, where ci∈{−1,0,1}c_i \in \{ -1,0,1 \}. Denote NN the number of positive integer roots of f(x)=0f(x)=0 (counting multiplicity). If f(x)=0f(x)=0 has no negative integer roots, find the maximum of NN.
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