Sorry to say but you are wrong. 5^2 - 3^2 = 4^2 is also 5^2 - 3^2 = 2^4 that is every x^n can be easily described by the equation z^2 - y^2 = x^n. (Actually every integer is described by this equation for z-y=1). This is an EQUALITY. So pray tell me how one can change the difference of two squared terms to the difference of two terms raised to the same power as x^n. This was Fermat's insight which I'm sure a man of his mathematical ability turned into a proof. The unfounded ignorance that abounds on this topic astounds me!