Related papers: Fermats Last Theorem on Topological Fields
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 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
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 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…
We construct a computable, computably categorical field of infinite transcendence degree over the rational numbers, using the Fermat polynomials and assorted results from algebraic geometry. We also show that this field has an intrinsically…
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.
Let F be a totally real number field of odd degree. We prove several purely local criteria for the asymptotic Fermat's Last Theorem to hold over F, and also for the non-existence of solutions to the unit equation over F. For example, if 2…
Recent results of Freitas, Kraus, Sengun and Siksek, give sufficient criteria for the asymptotic Fermat's Last Theorem to hold over a specific number field. Those works in turn build on many deep theorems in arithmetic geometry. In this…
We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.
We prove under some assumptions that the Tate conjecture holds for products of Fermat varieties of different degrees.
We give again the proof of several classical results concerning the cyclotomic approach to Fermat's last theorem using exclusively class field theory (essentially the reflection theorems), without any calculations. The fact that this is…
In the present paper we study, in a mathematically non-formal way, the validity of the Fermat's Last Theorem (FLT) by generalizing the usual procedure of extracting the square root of non convenient objects initially introduced by P. A. M.…
Assuming two deep but standard conjectures from the Langlands Programme, we prove that the asymptotic Fermat's Last Theorem holds for imaginary quadratic fields Q(\sqrt{-d}) with -d=2, 3 mod 4. For a general number field K, again assuming…
In this paper we obtain bounds for integer solutions of quadratic polynomials in two variables that represent a natural number. Also we get some results on twin prime numbers. In addition, we use linear functionals to prove some results of…
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
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.
We extend our sum over topologies formula to fermions. We show that fermionic fields display an instability with respect to topology fluctuations. We present some phenomenological arguments for a modification of the action in the case of…
Recent results concerning the relation of topology and low-lying fermion modes are summarized.