MathDB

Call a polynomial with real roots n-local if the greatest difference between any pair of its roots is

n

. Let

f(x)=x^2+ax+b

be a 1-local polynomial with distinct roots such that

a

and

b

are non-zero integers. If

f(f(x))

is a 23-local polynomial, find the sum of the roots of

f(x)

.
Proposed by Anthony Yang

Problem Statement