# Fermat's Last Theorem

## History

Fermat's last theorem is particularly famous in number theory. It was proposed by Fermat in the margin of his book Arithmetica. The note in the margin (when translated) read: "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." However, nobody was able to prove this theorem for centuries. Finally, in 1993 Andrew Wiles produced a proof of the theorem - a proof that was much more complicated than anything Fermat could have produced himself.

## The Theorem

Given integers $a,b,c$ and $n$, with $n \geq 3$ there are no solutions to the equation:

$\displaystyle a^n + b^n = c^n$