相关论文: Pell Numbers with Lehmer property

In the paper it is demonstrated that Bells theorem is an unprovable theorem.

We present a proof of Kemer's representability theorem for affine PI algebras over a field of characteristic zero.

This paper provides a proof of a LLT-like test for Fermat numbers, based on the properties of Lucas Sequences and on the method of Lehmer.

We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.

We give a cohomological characterisation of expander graphs, and use it to give a direct proof that expander graphs do not have Yu's property A.

In this paper we give purely geometrical proofs of the well-known properties of the lemniscate of Bernoulli.

In this paper, we study some properties of umbral calculus related to Appell sequence. From those properties, we derive new and interesting identities of Frobenius-Euler polynomials.

In this paper, we consider central complete and incomplete Bell polynomials which are generalizations of the recently introduced central Bell polynomials and central analogues for the complete and incomplete Bell polynomials. We investigate…

We prove that there is no class-dual for almost all sublinear models on graphs.

Let $F$ be a global function field of characteristic $p>0$ and $A/F$ an abelian variety. Let $K/F$ be an $\l$-adic Lie extension ($\l\neq p$) unramified outside a finite set of primes $S$ and such that $\Gal(K/F)$ has no elements of order…

We establish a function field analogue of Mertens' formula for Euler products restricted to primes in arithmetic progressions over the polynomial ring F_q[t]. Our results are in direct correspondence with those of Languasco and Zaccagnini…

It is a classical result from Diophantine approximation that the set of badly approximable numbers has Lebesgue measure zero. In this paper we generalise this result to more general sequences of balls. Given a countable set of closed…

We prove the splitting of the Kummer exact sequence and related exact sequences in arithmetic geometry.

We construct explicit resolutions of Weyl modules by divided powers and of co-Specht modules by permutational modules. We also prove a conjecture of Boltje-Hartmann on resolutions of co-Specht modules.

We provide a combinatorial interpretation of Lah numbers by means of planar networks. Henceforth, as a conesquence of Lindstr\"om's lemma, we conclude that the related Lah matrix possesses a remarkable property of total non-negativity.

Various sequences that possess explicit analytic expressions can be analysed asymptotically through integral representations due to Lindel\"of, which belong to an attractive but somewhat neglected chapter of complex analysis. One of the…

A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number--theoretical properties. A new class of…

We introduce polynomial sets of $(p,q)$-Appell type and give some of their characterizations. The algebraic properties of the set of all polynomial sequences of $(p,q)$-Appell type are studied. Next, we give a recurrence relation and a…

Let P be the set of the sequence of polynomials of degree n. The aim of this paper is to study the Stirling numbers of the second kind associated with P and of the first kind associated with P, in a unified and systematic way with the help…

Let $\ell\geq 5$ be prime. Let $\mathcal{F}_\ell$ be the collection of (isomorphism classes of) pure number fields $\mathbb{Q}(\sqrt[\ell]{a})$ of degree $\ell$, ordered by the absolute value of their discriminant. In 2018, Benli proved a…