Fermat's Last Theorem, (or Conjecture), was finally proven in 1995, some 360 years after its proposal in the margin of a book, "Arithmetica" by the Greek mathematician Diophantus, that Pierre de Fermat was reading at the time.

This proof, published by Andrew Wiles, a professor of mathematics at Princeton University, was a proof by association in that, by proving another conjecture, the Taniyama - Shimura Conjecture, Wiles also proved Fermat's Last Theorem via a link between the two, previously established by two other mathematicians, Gerhard Frey and Ken Ribet. The proof was extremely long and complex utilising the most modern 20^th Century analytical techniques, the majority of which would not have been available in Fermat's day.

Consequently, although the Fermat Conjecture was at last proven, there remained the tantalising question as to whether it could ever be proven in a direct manner, using only elementary analytical methods. It is the purpose of this paper to provide such a proof.