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Title: | A simple analytical proof of Fermat’s last theorem for n = 7 |
Authors: | Piyadasa, R.A.D. |
Issue Date: | 2010 |
Publisher: | Research Symposium 2010 - Faculty of Graduate Studies, University of Kelaniya |
Citation: | Research Symposium; 2010 :103-105pp |
Abstract: | It is well known that proof of Fermat’s last theorem for any odd prime is difficult and first proof for n 7 was given by Lame [1] ,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 2.7.115 is not a prime, whereas 2.5111 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 [3] 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. |
URI: | http://repository.kln.ac.lk/handle/123456789/4753 |
Other Identifiers: | Mathematics |
Appears in Collections: | ARS - 2010 |
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