Wrapped in [latex] shortcodes

In the 17th century, Pierre de Fermat had discovered many intriguing results about them, such as the fact that every prime number of the form [latex]4n + 1[/latex] for some integer n is a sum of two squares. For example, [latex]5 = 4 \times 1 + 1 = 2^2 + 1^2[/latex]  and [latex]13 = 4 \times 3 + 1 = 3^2 + 2^2[/latex]. He also had a proof that there are no integers [latex]x, y, z[/latex] greater than 1, such that

[latex]x^4 + y^4 = z^4.[/latex]

He had even incautiously committed himself to the statement that there are no integers x, y, z greater than 1, such that

[latex]x^n + y^n = z^n.[/latex]

for any integer [latex]n[/latex] other than 1 or 2.