Fermat's Last Theorem on an + bn = cn never works for any integers greater than two. Pierre de Fermat wrote that he had a proof for this theorem but no one has ever discovered it. No one has ever been able to reproduce the proof since, until mathematician, Andrew Wiles, developed a proof in 1994, fulfilling a dream he had since childhood.
Wiles achieved this great feat using the Taniyama-Shimura conjecture proposed in 1955. Sadly, Taniyama committed suicide in 1958. However, Shimura did live to witness Wiles's use of their conjecture in his proof of Fermat's Last Theorem.
Anyway, it is remarkable that Wiles was able to develop this proof, but Wiles used a 20th Century conjecture to develop his proof, so we know that this is not the same proof that Fermat had worked out since he worked it out in the 17th Century. So what was his Fermat's proof? Will we ever know if it truly existed, and/or what it was?
Fermat's last theorem can be proved using elementary Mathematics.One I have designed can be read on the internet:A simple and short analytical proof of Fermat's last theorem or CMNSEM,Vol.2,No.3,March 2011,pp.57-63.
ReplyDeleteWe must look for simpler ones still further.