Let be positive integers such that . If , then , which implies , a contradiction since must be positive. Therefore, we must have .
Let for some positive integer . Then
We know that . Let . Then and .
Let be a prime such that . Then divides but does not divide .
Since , we must have or .
Suppose . Then . Then .
Since and , then for some integer . Then .
If , then , which implies since . Thus for some integer , and .
Then .
However, does not divide .