Related papers: Wolstenholme again
In a recent article, Apagodu and Zeilberger (http://arxiv.org/abs/1606.03351)discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequence. At the…
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
In this paper, we construct an analogy of holonomy of connection to simplicial sets using A-infinity-categories. To construct it, we develop fiberwise integrals on simplicial sets and define an iterated integral on simplicial sets. It is an…
We consider row sequences of simultaneous rational approximations constructed in terms of Fourier expansions and prove a Montessus de Ballore type theorem.
In this paper we discuss an analogue of the Kac-Weisfeiler conjecture for a certain class of almost commutative algebras. In particular, we prove the Kac-Weisfeiler type statement for rational Cherednik algebras.
A proof of Sendov's conjecture is given.
We give a classification theorem for a relevant class of $t$-structures in triangulated categories, which includes in the case of the derived category of a Grothendieck category, the $t$-structures whose hearts have at most $n$ fixed…
Let K be an abstract elementary class satisfying the joint embedding and the amalgamation properties. Let m be a cardinal above the the L\"owenheim-Skolem number of the class. Suppose K satisfies the disjoint amalgamation property for limit…
Let B_n denote the nth Bell number. We use well-known recursive expressions for B_n to give a generalizing recursion that can be used to prove Touchard's congruence.
We upgrade Howard's divisibility toward Perrin-Riou's Heegner point Main Conjecture to an equality under some mild conditions. We do this by exploiting Wei Zhang's proof of the Kolyvagin conjecture. The main ingredient is an improvement of…
A very simple but useful almost sure convergence theorem of probability is given.
Let $\pi$ be a set of primes. By H.Wielandt definition, {\it Sylow $\pi$-theorem} holds for a finite group $G$ if all maximal $\pi$-subgroups of $G$ are conjugate. In the paper, the following statement is proven. Assume that $\pi$ is a…
We present short proofs of Toru\'nczyk's well-known characterization theorems of the Hilbert cube and Hilbert space, respectively.
We present a new and useful congruence identity satisfied by m-permutable varieties.
We give a proof of some small weight and level cases of Serre's conjecture.
In this paper a new conjecture equivalent to Collatz conjecture is presented. In particural, showing that (all) the solution(s) of newly introduced iterative functional equation(s) have a given property is equivalent to prove Collatz…
We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
In this paper we prove the existence of all higher logarithms as multivalued and ordinary Deligne cohomology classes.