The general quasi-order algorithm in number theory.
The generalization and proof of Bertrand's postulate.
The Generation of Arithmetical Identities.
The geometry of non-unit Pisot substitutions
It is known that with a non-unit Pisot substitution one can associate certain fractal tiles, so-called Rauzy fractals. In our setting, these fractals are subsets of a certain open subring of the adèle ring of the associated Pisot number field. We present several approaches on how to define Rauzy fractals and discuss the relations between them. In particular, we consider Rauzy fractals as the natural geometric objects of certain numeration systems, in terms of the dual of the one-dimensional realization...
The Gergonne -pile trick and the base counting system. (El truco de pilas de Gergonne y el sistema de numeración de base .)
The Golomb space is topologically rigid
The Golomb space is the set of positive integers endowed with the topology generated by the base consisting of arithmetic progressions with coprime . We prove that the Golomb space is topologically rigid in the sense that its homeomorphism group is trivial. This resolves a problem posed by T. Banakh at Mathoverflow in 2017.
The greatest common divisor of two recursive functions.
The greatest prime factor of
The Gross-Koblitz formula revisited
The integral mean of the sum-of-digits function of the Ostrowski expansion
The joint distribution of q-additive functions
The joint distribution of the binary digits of integer multiples
The Kazandzidis supercongruences. A simple proof and an application
The largest subset in [1,n] whose integers have pairwise l.c.m. not exceeding n, II
The least pair of consecutive character non-residues.
The Length of Periodic Continued Fractions.
The Lucas congruence for Stirling numbers of the second kind
0. Introduction. The numbers introduced by Stirling in 1730 in his Methodus differentialis [11], subsequently called “Stirling numbers” of the first and second kind, are of the greatest utility in the calculus of finite differences, in number theory, in the summation of series, in the theory of algorithms, in the calculation of the Bernstein polynomials [9]. In this study, we demonstrate some properties of Stirling numbers of the second kind similar to those satisfied by binomial coefficients; in...
The mantissa distribution of the primorial numbers
We show that the sequence of mantissas of the primorial numbers Pₙ, defined as the product of the first n prime numbers, is distributed following Benford's law. This is done by proving that the values of the first Chebyshev function at prime numbers are uniformly distributed modulo 1. We provide a convergence rate estimate. We also briefly treat some other sequences defined in the same way as Pₙ.
The number of binomial coefficients in residue classes modulo p and .
The number of crossings in a regular drawing of the complete bipartite graph.