Related papers: On a Possible Generalization of Fermats Last Theor…
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
We prove some new results related to Tanaka's formula.
This research focuses on the Numerical approach for Fermat's Last theorem. We can induce an Alternative form of Fermat's last theorem by using particular geometric mapping $\mathcal{M}$ on a Cartesian plane to a Torus. It transforms the…
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…
We give a generalization of Fujisawa's theorem in [F]. Our proof of the generalized theorem is purely algebraic and it is simpler than his proof.
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
We prove a generalization of Fulton's conjecture which relates intersection theory on an arbitrary flag variety to invariant theory.
This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.
In this paper, we investigate the extent to which the Bump-Hoffstein conjecture could be generalized for central coverings of general linear groups. We provide evidence for such generalized Bump-Hoffstein conjecture by proving some special…
We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.
A simple proof of Atanassov's Conjecture is presented. Atanassov's Conjecture is a generalization of Sperner's Lemma, a lemma which has been used to prove Brouwer's Fixed Point Theorem, among other fixed point theorems. The proof of…
We survey the classical results of the Dirichlet Approximation Theorem.
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…
The purpose of this paper is to present a generalization of Forelli's theorem. In particular, we prove an all dimensional version of the two-dimensional theorem of Chirka of 2005.
We survey recent developments on the Restriction conjecture.