MathDB

Let

a_1, a_2, \dots, a_{2020}

and

b_1, b_2, \dots, b_{2020}

be real numbers(not necessarily distinct). Suppose that the set of positive integers

n

for which the following equation:

|a_1|x-b_1|+a_2|x-b_2|+\dots+a_{2020}|x-b_{2020}||=n

(1) has exactly two real solutions, is a finite set. Prove that the set of positive integers

n

for which the equation (1) has at least one real solution, is also a finite set.

Problem Statement