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max no of roots of x^{20} + a_{19}x^{19} + ... + a_1x + a_0 in (99, 100)

Source: 2022 Grand Duchy of Lithuania, MC p1 (Baltic Way TST) https://artofproblemsolving.com/community/c1321893_grand

November 17, 2022
algebrapolynomial

Problem Statement

Given a polynomial with integer coefficients P(x)=x20+a19x19+...+a1x+a0,P(x) = x^{20} + a_{19}x^{19} +... + a_1x + a_0, having 2020 different real roots. Determine the maximum number of roots such a polynomial PP can have in the interval (99,100)(99, 100).
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