Related papers: Wolstenholme again
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
We establish a q-analogue of Wolstenholme's harmonic series congruence.
In this paper, we state and prove some congruence properties for the trinomial coeficients, one of which is similar to the Wolstenholme's theorem.
We prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial.
We provide a proof of Wilson's Theorem and Wolstenholme's Theorem based on a direct approach by Lagrange requiring only basic properties of the primes and the Binomial theorem. The goal is to show how similar the two theorems are by…
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
We present a detailed proof of Wolstenholme's theorem using an Egorychev-type contour integral and an exponential change of variables. All formal series manipulations are justified, and the connection with harmonic sums and Bernoulli…
Given a prime p and a positive integer m satisfying a certain inequality, the converse of Wolstenholme's Theorem is shown to hold for the product mp^k where k is any positive integer, generalizing a result by Helou and Terjanian.
We give a generalization of Wolstenholme's harmonic series congruence for the Lucas sequences.
We show some new Wolstenholme type $q$-congruences for some classes of multiple $q$-harmonic sums of arbitrary depth with strings of indices composed of ones, twos and threes. Most of these results are $q$-extensions of the corresponding…
We give an elementary proof of the Selberg identity for Kloosterman sums, which only requires the orthogonality of additive characters.
We verify a confluence result for the rewriting calculus of the linear category introduced in our previous paper. Together with the termination result proved therein, the generalized coherence theorem for linear category is established.…
Using generalized binomial coefficients with respect to fundamental Lucas sequences we establish congruences that generalize the classical congruence of Wolstenholme and other related stronger congruences.
We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.
We show that the framing of $2$-sequences whose generating functions are rational integrate to $3$-sequences. To do so, we give a generalization of Wolstenholme's Theorem.
We prove several congruences for trinomial coefficients.
In their study of a binomial sum related to Wolstenholme's theorem, Chamberland and Dilcher prove that the corresponding sequence modulo primes $p$ satisfies congruences that are analogous to Lucas' theorem for the binomial coefficients…
We prove some symmetric $q$-congruences.
We prove several Stern's type congruences for generalized bernoulli numbers.
We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of…