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### A cellular automaton on a torus.

Portugaliae Mathematica

Integers

### A characterization of sequences with the minimum number of k-sums modulo k

Colloquium Mathematicae

Let G be an additive abelian group of order k, and S be a sequence over G of length k+r, where 1 ≤ r ≤ k-1. We call the sum of k terms of S a k-sum. We show that if 0 is not a k-sum, then the number of k-sums is at least r+2 except for S containing only two distinct elements, in which case the number of k-sums equals r+1. This result improves the Bollobás-Leader theorem, which states that there are at least r+1 k-sums if 0 is not a k-sum.

### A complete annotated bibliography of work related to Sidon sequences.

The Electronic Journal of Combinatorics [electronic only]

Acta Arithmetica

### A Distribution Property of the Sequences of Lucas Numbers.

Elemente der Mathematik

### A function related to the rumor sequence conjecture.

Journal of Integer Sequences [electronic only]

### A general notion of independence of sequences of integers.

International Journal of Mathematics and Mathematical Sciences

### A note on p-adic valuations of Schenker sums

Colloquium Mathematicae

A prime number p is called a Schenker prime if there exists n ∈ ℕ₊ such that p∤n and p|aₙ, where $aₙ={\sum }_{j=0}^{n}\left(n!/j!\right){n}^{j}$ is a so-called Schenker sum. T. Amdeberhan, D. Callan and V. Moll formulated two conjectures concerning p-adic valuations of aₙ when p is a Schenker prime. In particular, they conjectured that for each k ∈ ℕ₊ there exists a unique positive integer ${n}_{k}<{5}^{k}$ such that $v₅\left({a}_{m·{5}^{k}+{n}_{k}}\right)\ge k$ for each nonnegative integer m. We prove that for every k ∈ ℕ₊ the inequality v₅(aₙ) ≥ k has exactly one solution modulo ${5}^{k}$. This confirms the...

### A search for Tribonacci-Wieferich primes

Acta Mathematica Universitatis Ostraviensis

Such problems as the search for Wieferich primes or Wall-Sun-Sun primes are intensively studied and often discused at present. This paper is devoted to a similar problem related to the Tribonacci numbers.

Acta Arithmetica

### A special prime divisor of the sequence: $ah+b,a\left(h+1\right)+b,\cdots ,a\left(h+k-1\right)+b$.

International Journal of Mathematics and Mathematical Sciences

### An addition theorem on the cyclic group ${ℤ}_{{p}^{\alpha }{q}^{\beta }}$.

The Electronic Journal of Combinatorics [electronic only]

Integers

Acta Arithmetica

Acta Arithmetica

### Barycentric Ramsey numbers for small graphs.

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

### Catalan numbers modulo ${2}^{k}$.

Journal of Integer Sequences [electronic only]

Acta Arithmetica

### Covering densities

Mathematica Slovaca

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