Fermat's Last Theorem

Fermat's Last Theorem (FLT) states that there are no positive integers x, y, and z that satisfy the following Diophantine equation The French lawyer and mathematician Pierre de Fermat made this conjecture in 1637 in the margin of a copy of the book Arithmetica, an Ancient Greek mathematical text written by Diophantus of Alexandria in the 3rd century AD. Fermat famously conjectured he had a proof of Eq. 1, but it was too large to fit in the margin of the book. The English mathematician Andrew Wiles published the first successful proof of the conjecture in 1995, after more than 350 years of effort by some of the greatest mathematicians in history (see this link for more details). We will prove the particular case where n 4, which is the simplest one. However, before that, we need to prove the following simpler auxiliary theorem about Pythagorean triples (x, y, z).