Diophantine Equation $x^n+y^n=z^n$

Question

Problem

Using simple mathematical operators (+,- ,> etc.) can it be shown that (assuming $ x<y$) Fermat’s theorem is always true when $$ n\ge x$$

Request I am sure this approach has been discussed somewhere earlier. If anyone therefore could either direct me to such resource of discussion or show the proof. I have also developed a proof which I shall share tomorrow for a review.

Answer 1

$$x^n=z^n-y^n=(z-y)(z^{n-1}+yz^{n-2}+\cdots+y^{n-1})\ge ny^{n-1}\gt xx^{n-1}$$ contradiction.