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A Simple Proof on Fermat’s Last Theorem in Case of n=3

Keywords

Fermatƒ??s last theorem, n=3, { t min , t max } ‹Ÿ? { x min , x max }, algebraic equation, induction, disprove method.

Research Identity (RIN)

Journal

License

Attribution 2.0 Generic (CC BY 2.0)

English

Abstract

Fermatƒ??s last theorem was proposed more than 350 years ago, it attracted the interests of a lot of researchers[1-11]. The simplest case of Fermatƒ??s last theorem is n=3, but the previous proofs on it are generally complex or not easy to understand. The present work through the transformation x=t+1, firstly proves that when the values of x and t x and t ‹Ÿ? { t min , t max } ‹Ÿ? { x min , x max }, the Fermatƒ??s last theorem in case of n=3 is true. Furthermore, the paper also proves that when x take other positive integers besides x ‹Ÿ? { t min , t max } ‹Ÿ? { x min , x max }, the Fermatƒ??s last theorem in case of n=3 is true as well. Therefore, there are no a group of positive integers of x, y and z to satisfy the Diophantine equation in case of n=3; Fermatƒ??s last theorem in case of n=3 is true.

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Author avatar
Dr. Zhang Yue
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