Related papers: Fermat's Last Theorem and its another Proof
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.
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.
We take the perspective of an advanced high school student trying to understand the proof of Fermat's Last Theorem for the first time. We collect definitions and statements needed to summarise how Fermat's Last Theorem was first proved in…
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…
This paper presents a novel direct elementary proof for Fermat's Last Theorem. We use algebra, modular math, and binomial series to develop inherent mathematical relationships hidden within Fermat's Last Theorem. With these derived…
In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra and number theory.
We propose a new approach at Fermat's Last Theorem (FLT) solution: for each FLT equation we associate a polynomial of the same degree. The study of the roots of the polynomial allows us to investigate the FLT validity. This technique,…
In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra, geometry and number theory
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
We study Kummer's approach towards proving the Fermat's last Theorem for regular primes. Some basic algebraic prerequisites are also discussed in this report, and also a brief history of the problem is mentioned. We review among other…
A elementary proof of Fermat"s Last Theorem[1] is presented for the case of even exponents n=2q, where q is any integer, including 2. For even exponents, the proof of the theorem reduces to showing that solutions of the Pythagorean equation…
In this short article we do not prove Fermat's last theorem. We show that the number 2 is an exceptional number in this theorem.
Fermat's Last Theorem is proved by using the philosophical and mathematical knowledge of 1637 when the French mathematician Pierre de Fermat claimed to have a truly marvelous proof of his conjecture. Our approach consists of setting three…
`Fermat's Last Theorem for the exponent 3 has received numerous proofs, the most common of which being either in Euler's or in Gauss' style. This latter works entirely in the ring of integers of the quadratic field generated by the square…
We formalize a complete proof of the regular case of Fermat's Last Theorem in the Lean4 theorem prover. Our formalization includes a proof of Kummer's lemma, that is the main obstruction to Fermat's Last Theorem for regular primes. Rather…
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…
We formalise the proof of the first case of Fermat's Last Theorem for regular primes using the \emph{Lean} theorem prover and its mathematical library \emph{mathlib}. This is an important 19th century result that motivated the development…
An alternative form of Fermats equation[1] is proposed. It represents a portion of the identity that includes three terms of Fermats original equation. This alternative form permits an elementary and compact proof of the first case of…
In this paper two conjectures are proposed based on which we can prove the first case of Fermat's Last Theorem(FLT) for all primes $p \equiv -1 (\bmod~6)$. With Pollaczek's result {\bf [1]} and the conjectures the first case of FLT can be…
The main result of the present article is a proof of Fermat's Last Theorem for sufficiently large prime exponents $p$ with $p \equiv 2 \pmod{3}$ over certain number fields. A particular case of these fields are the maximal real subfields of…