On a Possible Generalization of Fermats Last Theorem

In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture.

We show that an elementary proof of Fermat's Last Theorem (FLT) exists. Our paper also extends the scope of FLT from integers to all rational numbers.

In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra, geometry and number theory

In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra and number theory.

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor was offered as being, possibly the proof Fermat had in mind. The present proof being brief, direct and concise is a candidate for being what Fermat had in mind. It is also completely accessible to any one trained in common algebra. That criti...

Fermat's Last Theorem states that the Diophantine equation $X^n+Y^n=Z^n$ has no non-trivial solution for any $n$ greater than 2. In this paper we give a brief and simple proof of the theorem using only elementary methods.

This paper has been withdrawn by the author [arXiv admin].

The $abc$ conjecture is a very deep concept in number theory with wide application to many areas of number theory. In this article we introduce the conjecture and give examples of its applications. In particular we apply the $abc$ conjecture to the location of powerful numbers.

We present an elementary proof of Fermat's Last Theorem. No ancillary results are used, not even the most basic ones. The proof directly leads to a contradiction of the Fermat equation in the set of integers.