ABSTRACT
We are now ready to tackle number theory in Euclidean rings other than Z . Our motivation is that polynomials such as
factor more completely over extension rings of Z and thereby may enable us to solve equations more readily by means of these larger rings. We shall illustrate this fact in two famous results related to the famous French mathematician Pierre Fermat. Actually Fermat was a jurist by profession and never published his proofs; nevertheless, we believe that he knew the proofs, since there is only one mistake he is known to have made in his mathematical career.
