Page 1 Next

## Displaying 1 – 20 of 149

Showing per page

### $0\text{-}1$ sequences having the same numbers of $\left(1\text{-}1\right)$-couples of given distances

Mathematica Bohemica

Let $a$ be a $0-1$ sequence with a finite number of terms equal to 1. The distance sequence ${\delta }^{\left(a\right)}$ of $a$ is defined as a sequence of the numbers of $\left(1-1\right)$-couples of given distances. The paper investigates such pairs of $0-1$ sequences $a,b$ that a is different from $b$ and ${\delta }^{\left(a\right)}={\delta }^{\left(b\right)}$.

Acta Arithmetica

### A generalization of Beatty's theorem.

Southwest Journal of Pure and Applied Mathematics [electronic only]

### A generalization of some results in additive number theory.

Mathematische Zeitschrift

Acta Arithmetica

### A nontransformation proof of Mann's density theorem.

Journal für die reine und angewandte Mathematik

Acta Arithmetica

### A note on uniform or Banach density

Annales mathématiques Blaise Pascal

In this note we present and comment three equivalent definitions of the so called uniform or Banach density of a set of positive integers.

Acta Arithmetica

### A problem of Rankin on sets without geometric progressions

Acta Arithmetica

A geometric progression of length k and integer ratio is a set of numbers of the form $a,ar,...,a{r}^{k-1}$ for some positive real number a and integer r ≥ 2. For each integer k ≥ 3, a greedy algorithm is used to construct a strictly decreasing sequence ${\left({a}_{i}\right)}_{i=1}^{\infty }$ of positive real numbers with a₁ = 1 such that the set ${G}^{\left(k\right)}={\bigcup }_{i=1}^{\infty }\left({a}_{2i},{a}_{2i-1}\right]$ contains no geometric progression of length k and integer ratio. Moreover, ${G}^{\left(k\right)}$ is a maximal subset of (0,1] that contains no geometric progression of length k and integer ratio. It is also proved that there is...

Integers

### A theorem of H. Steinhaus and $\left(R\right)$-dense sets of positive integers

Czechoslovak Mathematical Journal

### Abschätzung der Dichte von Summenmengen.

Mathematische Zeitschrift

### Additive properties of dense subsets of sifted sequences

Journal de théorie des nombres de Bordeaux

We examine additive properties of dense subsets of sifted sequences, and in particular prove under very general assumptions that such a sequence is an additive asymptotic basis whose order is very well controlled.

Integers

Acta Arithmetica

### Arithmetic progressions, prime numbers, and squarefree integers

Czechoslovak Mathematical Journal

In this paper we establish the distribution of prime numbers in a given arithmetic progression $p\equiv l\phantom{\rule{4.44443pt}{0ex}}\left(mod\phantom{\rule{0.277778em}{0ex}}k\right)$ for which $ap+b$ is squarefree.

### Asymptotic densities of sets of positive integers

Mathematica Slovaca

Acta Arithmetica

### Atkin's theorem on pseudo-squares.

Publications de l'Institut Mathématique. Nouvelle Série

Page 1 Next