Proof of Fermat’s Last Theorem for n=3 Using Tschirnhaus Transformation

DOI: 10.5176/2251-3388_2.2.45

Authors: B.B.Upeksha P. Perera, and R.A.D. Piyadasa

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 non-rational roots it was concluded that the Fermat’s equation cannot have integer solutions.

Keywords: Fermat’s Last Theorem; Tschirnhaus transformation; Integer roots