I am a second year doctoral student in mathematics at the University of Central Florida in Orlando, FL. I obtained my MS from WKU in Bowling Green, KY where I researched continued radicals and Cantor sets.
It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not distained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts.