Representations of integers as sums of primes from a Beatty sequence
Running modulus recursions.
Sets with even partition functions and 2-adic integers. II.
Short remark on Fibonacci-Wieferich primes
This paper has been inspired by the endeavour of a large number of mathematicians to discover a Fibonacci-Wieferich prime. An exhaustive computer search has not been successful up to the present even though there exists a conjecture that there are infinitely many such primes. This conjecture is based on the assumption that the probability that a prime is Fibonacci-Wieferich is equal to . According to our computational results and some theoretical consideratons, another form of probability can...
Some Borel measures associated with the generalized Collatz mapping
This paper is a continuation of a recent paper [2], in which the authors studied some Markov matrices arising from a mapping T:ℤ → ℤ, which generalizes the famous 3x+1 mapping of Collatz. We extended T to a mapping of the polyadic numbers and construct finitely many ergodic Borel measures on which heuristically explain the limiting frequencies in congruence classes, observed for integer trajectories.
Some remarks on the equation in Fibonacci numbers.
Stapled sequences and stapling coverings of natural numbers.
Subsequence sums of zero-sum free sequences over finite abelian groups
Let G be a finite abelian group of rank r and let X be a zero-sum free sequence over G whose support supp(X) generates G. In 2009, Pixton proved that for r ≤ 3. We show that this result also holds for abelian groups G of rank 4 if the smallest prime p dividing |G| satisfies p ≥ 13.
Subset sums modulo a prime
Sum-product estimates applied to Waring's problem mod .
Sums of distinct residues mod p
Sumsets in quadratic residues
We describe all sets which represent the quadratic residues in the sense that R = A + A or R = A ⨣ A. Also, we consider the case of an approximate equality R ≈ A + A and R ≈ A ⨣ A and prove that A is then close to a perfect difference set.
Sur les fonctions additives à valeurs entières
The complexity of uniform distribution
The distribution of second order linear recurrence sequences mod
The Gergonne -pile trick and the base counting system. (El truco de pilas de Gergonne y el sistema de numeración de base .)
The number of k-sums of abelian groups of order k
The structure of maximal zero-sum free sequences
The terms of the form 7kx² in the generalized Lucas sequence with parameters P and Q
Let Vₙ(P,Q) denote the generalized Lucas sequence with parameters P and Q. For all odd relatively prime values of P and Q such that P² + 4Q > 0, we determine all indices n such that Vₙ(P,Q) = 7kx² when k|P. As an application, we determine all indices n such that the equation Vₙ = 21x² has solutions.
Tribonacci modulo and
Our previous research was devoted to the problem of determining the primitive periods of the sequences where is a Tribonacci sequence defined by an arbitrary triple of integers. The solution to this problem was found for the case of powers of an arbitrary prime . In this paper, which could be seen as a completion of our preceding investigation, we find solution for the case of singular primes .