According to Fermat's Last Theorem, have no solutions in positive integers, if n is an integer greater than 2.
But I can (hopefully) only prove .
Expand and you will get
Any integer can be expressed as .
Hence, let be
Dividing both sides by
Expanding , you will get
Simplifying the equation,
Hence, and any integer.
any integer and .
But anybody know that can be a solution.
Note that is a neutral number
Now consider the case,
Where is any integer.
Using graph theory it is easy to realise that there are no rational solutions.
If interested, view Leonhard Euler's proof of this.