Abstract
This paper gives a proof on Fermat’s last theorem (FLT) for n = 3 by firstly reducing the Fermat’s equation to a cubic equation of one variable and then using Tschirnhaus transformation to reduce it to a depressed cubic. By showing that this last equation has nonrational roots, it was concluded that the Fermat’s equation cannot have integer solutions.
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Piyadasa, R.A.D., Shadini, A.M.D.M., Jayasinghe, W.J.M.L.P.: Simple analytical proofs of three Fermat’s theorems. Can. J. Comput. Math. Nat. Sci. Eng. Med. 2(3) (2011) [Online]. http://www.ampublisher.com/Mar%202011/CMNSEM-1103-014.pdf. Accessed 19 Sept 2013
Tschirnhaus, E.W.: A method for removing all intermediate terms from a given equation. ACM SIGSAM Bull. 37(1) (2003) (Translated by R. F. Green) [Online]. http://www.sigsam.org/bulletin/articles/143/tschirnhaus.pdf. Accessed 19 Sept 2013
Piyadasa, R.A.D.: Mean value theorem and Fermat’s last theorem for n = 3. In: Proceedings of the Annual Research Symposium 2007, Faculty of Graduate Studies, University of Kelaniya [Online]. http://www.kln.ac.lk/uokr/ARS2007/4.6.pdf. Accessed 15 Nov 2013
Piyadasa, R.A.D.: Simple and analytical proof of Fermat’s last theorem for n = 3. In: Proceedings of the Annual Research Symposium 2008, Faculty of Graduate Studies, University of Kelaniya [Online]. http://www.kln.ac.lk/uokr/ARS2008/4.20.pdf. Accessed 15 Nov 2013]
Piyadasa, R.A.D.: Method of infinite descent and proof of Fermat’s last theorem for n = 3. J. Comput. Math. Nat. Sci. Eng. Med. 1(6) (2010). http://www.ampublisher.com/September%202010/CMNSEM-1009-012.pdf. Accessed 19 Sept 2013
Piyadasa, R.A.D.: A simple and short analytical proof of Fermat’s last theorem. Can. J. Comput. Math. Nat. Sci. Eng. Med. 2(3) (2011) [Online]. http://www.ampublisher.com/Mar%202011/CMNSEM-1103-015.pdf. Accessed 19 Sept 2013
Weisstein, E.W.: Vieta’s substitution. From MathWorld—a Wolfram web resource [Online]. http://mathworld.wolfram.com/VietasSubstitution.html. Accessed 19 Sept 2013
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Perera, B.B.U., Piyadasa, R.A.D. (2016). Proof of Fermat’s Last Theorem for n = 3 Using Tschirnhaus Transformation. In: Chen, K., Ravindran, A. (eds) Forging Connections between Computational Mathematics and Computational Geometry. Springer Proceedings in Mathematics & Statistics, vol 124. Springer, Cham. https://doi.org/10.5176/2251-1911_CMCGS14.34_12
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DOI: https://doi.org/10.5176/2251-1911_CMCGS14.34_12
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16138-9
Online ISBN: 978-3-319-16139-6
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