Related papers: Wolstenholme again

We give an elementary, self-contained and quick proof of Belyi's theorem. As a by-product of our proof we obtain an explicit bound for the degree of the defining number field of a Belyi surface.

We give a short proof to the following tilting theorem by Happel, Reiten and Smal{\o} via an explicit construction: given two abelian categories $\mathcal{A}$ and $\mathcal{B}$ such that $\mathcal{B}$ is tilted from $\mathcal{A}$, then…

We give a purely combinatorial proof of the density Hales--Jewett Theorem that is modeled after Polymath's proof but is significantly simpler. In particular, we avoid the use of the equal-slices measure and work exclusively with the uniform…

We give a complete and careful proof of Quillen's theorem on the existence of the standard model category structure on the category of topological spaces. We do not assume any familiarity with model categories.

In this paper we derive congruences expressing Bell numbers and derangement numbers in terms of each other modulo any prime.

Holonomy algebras of Weyl connections in Lorentzian signature are classified. In particular, examples of Weyl connections with all possible holonomy algebras are constructed.

The Ghahramani-Lau conjecture is established; in other words, the measure algebra of every locally compact group is strongly Arens irregular. To this end, we introduce and study certain new classes of measures (called approximately…

In this note, we prove the coherence of Frobenius stable direct images in a new case. We also show a generation theorem regarding to it. Furthermore, we prove a corresponding theorem in characteristic zero.

The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.

We extend a result of Ahlgren and Ono on congruences for traces of singular moduli of level 1 to traces defined in terms of Hauptmodul associated to certain groups of genus 0 of higher levels.

We provide new and purely combinatorial proofs of two infinite extensions of the Hales--Jewett theorem. The first one is due to T. Carlson and S. Simpson and the second one is due T. Carlson. Both concern infinite increasing sequences of…

We give a short, mostly elementary and self-contained proof of the classical result that the groups of diffeomorphisms, homeomorphisms, and homotopy equivalences of a surface have the same group of connected components.

Let $H$ be a connected graded Hopf algebra over a field of characteristic zero and $K$ an arbitrary graded Hopf subalgebra of $H$. We show that there is a family of homogeneous elements of $H$ and a total order on the index set that satisfy…

We prove various congruences for Catalan and Motzkin numbers as well as related sequences. The common thread is that all these sequences can be expressed in terms of binomial coefficients. Our techniques are combinatorial and algebraic:…

In this paper we present a combinatorial proof of Selberg's integral formula. We start by giving a bijective proof of a Theorem about the number of topological orders of a certain related directed graph. Selberg's Integral Formula then…

We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.

Modules for sesquiads and congruence schemes are introduced. It is shown that the corresponding categories are belian and that base change functors establish an ascent datum which allows for a cohomology theory to be established.

We settle in the affirmative the Graham-Sloane conjecture.

We prove the decidability of the elementary theory of a free group.

We obtain recurrences for smallest parts functions which resemble Euler's recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holomorphic modular forms of weight 2.