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.