Pythagorean Triples and Fermat�s Last Theorem Proven in One Page

Abstract

We attempt to obtain Pythagorean triples by a simple method consisting in transforming the relation between integers  into an equation in by introduction of a parameter . By this way we obtain easily Pythagorean triples for each choice of  . Following this example we introduce also a suitable parameter  totransform the relation  into an equation in  which must have only one multiple root, i.e. must have coefficients alternated in signs. Observing that this happens only for  and not at all for  , we arrive to conclude that the equation has roots only for   and no root for  thus prove the Fermats last theorem.