MathDB

We say that a set

S

of integers is rootiful if, for any positive integer

n

and any

a_0, a_1, \cdots, a_n \in S

, all integer roots of the polynomial

a_0+a_1x+\cdots+a_nx^n

are also in

S

. Find all rootiful sets of integers that contain all numbers of the form

2^a - 2^b

for positive integers

a

and

b

Problem Statement