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# A simple analytical proof of Fermat’s last theorem for n = 7

 dc.contributor.author Piyadasa, R.A.D. dc.date.accessioned 2014-12-17T08:33:57Z dc.date.available 2014-12-17T08:33:57Z dc.date.issued 2010 dc.identifier Mathematics en_US dc.identifier.citation Research Symposium; 2010 :103-105pp en_US dc.identifier.uri http://repository.kln.ac.lk/handle/123456789/4753 dc.description.abstract It is well known that proof of Fermat’s last theorem for any odd prime is difficult and first en_US proof for n  7 was given by Lame  ,and Kumar also has given a proof for a special class of primes (Regular primes)which includes the case n  7 .However, these proofs are lengthy and difficult and may not easily be extended for all odd primes. The prime n  7 differs from n  5 since 2.7.115 is not a prime, whereas 2.5111 is a prime. Then it follows from the famous theorem of Germain Sophie that the corresponding Fermat’s equation , ( , ) 1 7 7 7 z  x  y x y  may have two classes of integer solutions, xyz  0(mod7) and xyz  0(mod7) if we assume that the Fermat equation has non-trivial integer solutions for x, y, z . This fact is proved using the simple argument  of Oosterhuis. The main objective of this paper is to give a simple analytical proof for the Fermat’s last theorem n  7 using general respective parametric solutions corresponding two classes of solutions of the Fermat equation ,which has already been extended for all odd primes. dc.language.iso en en_US dc.publisher Research Symposium 2010 - Faculty of Graduate Studies, University of Kelaniya en_US dc.title A simple analytical proof of Fermat’s last theorem for n = 7 en_US dc.type Article en_US
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