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

作　　者：Yufeng Xia 

机构地区：[1]Huaqiao University, Fujian, China

出　　处：《Advances in Pure Mathematics》2020年第3期125-154,共30页理论数学进展（英文）

摘　　要：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.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.

关 键 词：PYTHAGORAS THEOREM Fermat’s LAST THEOREM Geometric Method EQUATION of DEGREE n with One UNKNOWN 

分 类 号：O17[理学—数学]