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


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

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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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