MathDB

There's a special computer and it has a memory. At first, it's memory just contains

x

. We fill up the memory with the following rules.
1) If

f\neq 0

is in the memory, then we can also put

\frac{1}{f}

in it.
2) If

f,g

are in the memory, then we can also put

f+g

and

f-g

in it.
Find all natural number

n

such that we can have

x^n

in the memory.

Problem Statement