MathDB

The graph of the degree

2021

polynomial

P(x)

, which has real coefficients and leading coefficient

1

, meets the

x

-axis at the points

(1,0),\, (2,0),\,(3,0),\dots,\, (2020,0)

and nowhere else. The mean of all possible values of

P(2021)

can be written in the form

a!/b

, where

a

and

b

are positive integers and

a

is as small as possible. Compute

a+b

Problem Statement