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 2 22 ) na(ba  into an equation innby introduction of a parameter n /b  . By this way we obtain easily Pythagorean triples for each choice of  . Following this example we introduce also a suitable parameter  totransform the relation m mm ) na(ba  into an equation inn which must have only one multiple root, i.e. must have coefficients alternated in signs. Observing that this happens only for 2 ,1m  and not at all for 2 m , we arrive to conclude that the equation has roots only for 2 ,1m  and no root for 2 m thus prove the Fermat’s last theorem.

Author (s) Details

Dr. Do Tan Si
HoChiMinh-City Physical Association, Vietnam and ULB and UEM, Belgium.