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

We attempt to obtain Pythagorean triples by a simple method consisting in transforming the relation
between integers a2 b2( a  n )2 into an equation in nby introduction of a parameter  b / n . By this
way we obtain easily Pythagorean triples for each choice of . Following this example we introduce
also a suitable parameter totransform the relation am bm( a  n )m into an equation in n which must
have only one multiple root, i.e. must have coefficients alternated in signs. Observing that this
happens only for m  1,2 and not at all for m  2 , we arrive to conclude that the equation has roots only
for m  1,2 and no root for m  2 thus prove the Fermat’s last theorem.