Skip to main content

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 124))

  • 900 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. 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

  2. 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

  3. 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

  4. 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]

  5. 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

  6. 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

  7. Weisstein, E.W.: Vieta’s substitution. From MathWorld—a Wolfram web resource [Online]. http://mathworld.wolfram.com/VietasSubstitution.html. Accessed 19 Sept 2013

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. B. U. Perera .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

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

Download citation

Publish with us

Policies and ethics