MathDB
2020 BMT Individual 15

Source:

January 9, 2022
algebra

Problem Statement

The graph of the degree 20212021 polynomial P(x)P(x), which has real coefficients and leading coefficient 1, meets the x-axis at the points (1,0)(1, 0), (2,0)(2, 0), (3,0)(3, 0) , ...... , (2020,0)(2020, 0) and nowhere else. The mean of all possible values of P(2021)P(2021) can be written in the form a!/ba!/b, where aa and bb are positive integers and aa is as small as possible. Compute a+ba + b.
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