From Pythagoras Theorem to Fermat’s Last Theorem and the Relationship between the Equation of Degree <i>n</i> with One Unknown

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 a n + b n = c n that can never be integer; if a , b and c are integer and a ≠ b , n is integer and n > 2, the function a n + b n = c n cannot be established.