Yufeng Xia
Abstract The most interesting and famous problem that puzzled the mathematicians all around the world is much likely to be the Fermat’s Last Theorem. However, since the Theorem was proposed, people can’t find a way to solve the problem until Andrew Wiles proved the Fermat’s Last Theorem through a very difficult method called Modular elliptic curves in 1995. In this paper, I firstly constructed a geometric method to prove Fermat’s Last Theorem, and in this way we can easily get the conclusion below: If a and b are integer and a = b, n ∈ Q and n > 1, the value of c satisfies the function aⁿ + bⁿ = cⁿ that can never be integer; if a, b and c are integer and a ≠ b, n is integer and n > 2, the function aⁿ + bⁿ = cⁿ cannot be established.

Keywords Pythagoras Theorem, Fermat’s Last Theorem, Geometric Method, Equation of Degree n with One Unknown

Share and Cite: Xia, Y. (2020) From Pythagoras Theorem to Fermat’s Last Theorem and the Relationship between the Equation of Degree n with One Unknown. Advances in Pure Mathematics, 10, 125-154. doi: 10.4236/apm.2020.103009.

Yufeng Xia
Huaqiao University, Fujian, China.
DOI: 10.4236/apm.2020.103009   PDF   HTML   XML   420 Downloads   1.142 Views   Citations

https://www.scirp.org/journal/paperinformation.aspx?paperid=99095