Related papers: On certain positive integer sequences

In this article, we give an account of some recent irreducibility testing criteria for polynomials having integer coefficients over the field of rational numbers.

Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.

It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the…

In this note some properties of the sum of element orders of a finite abelian group are studied.

Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…

Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…

This is an expository article on recent developments in the theory of group relaxations in integer programming from an algebraic perspective.

This article provides a synthesis of recent advances in the study of the PI property in various classes of noncommutative algebras of polynomial type.

The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of…

These notes are our contribution to the Proceedings of the ICM 2026. We discuss some results we have obtained (in part jointly with coauthors) regarding the representation theory of reductive algebraic groups over algebraically closed…

Very recently, in [Das et al., J. Lond. Math. Soc., 2025], statistically characterized subgroups were studied for certain classes of non-arithmetic sequences. Subsequently, in [Das et al., Bull. Sci. Math., 2025], characterized subgroups…

In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.

We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all…

We survey and prove properties a family of recurrences bears in relation to integer representations, compositions, the Pascal triangle, sums of digits, Nim games and Beatty sequences.

In these notes we review recent progress (and, in Section \ref{sec:ados}, we announce a new result) concerning the statistical properties of the spectrum of Wigner random matrices.

Two types of finite series of products of harmonic numbers involving nonnegative integer powers are evaluated, also yielding two other important harmonic number identities. The recursion formulas for these sums are derived, which are easily…

In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…

Let $n,d$, and $k$ be positive integers where $n$ and $d$ are coprime. Our two main results are Theorem 1. There is a partition of the infinite interval $[kd,\infty)$ of positive integers into a family of finite sets $X$ for which the sum…

We axiomatize the first-order theories of exponential integer parts of real-closed exponential fields in a language with $2^x$, in a language with a predicate for powers of 2, and in the basic language of ordered rings. In particular, the…

This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…