Related papers: On a Possible Generalization of Fermats Last Theor…

In the present note a generalization of Borel-Cantelli Lemma is proposed.

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.

Recent work of Freitas and Siksek showed that an asymptotic version of Fermat's Last Theorem holds for many totally real fields. Later this result was extended by Deconinck to generalized Fermat equations of the form $Ax^p +By^p +Cz^p = 0$,…

In a recent paper, Freitas and Siksek proved an asypmtotic version of Fermat's Last Theorem for many totally real fields. We prove an extension of their result to generalized Fermat equations of the form $A x^p+B y^p+ C z^p=0$, where $A$,…

We review a combinatoric approach to the Hodge Conjecture for Fermat Varieties and announce new cases where the conjecture is true.

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

Several results about the union-closed sets conjecture are presented.

We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new…

A generalization of the law of total covariance is presented and proved.

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

This paper has been withdrawn by the author for further investigation.

We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.

Even though flt is a number theoretic result we prove that the result depends on the topological as well as the field structure of the underlying space.

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.

In this note we prove a more general (and topological) version of Gr\"unbaum's conjecture about affine invariant points. As an application of our result we show that, if we consider the action of the group of similarities, Gr\"unbaum's…

This paper has been withdrawn by the author [arXiv admin].

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 survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

In the paper, we generalize some congruences of Lehmer for general composite numbers.