On disjoint arithmetic progressions
On divisibility of Narayana numbers by primes.
On divisibility of the class number of real octic fields of a prime conductor by
The aim of this paper is to prove the following Theorem Theorem Let be an octic subfield of the field and let be prime. Then divides if and only if divides for some , , , .
On divisors of terms of linear recurrence sequences.
On Erdős-Ginzburg-Ziv inverse theorems
On exactly covering systems of congruences having moduli occurring at most twice
On Exponential Recurring Sequences.
On extensions of 1 chains
On extremal h-bases A...
On extremal sets without coprimes
On families of nonlinear recurrences related to digits.
On families of weakly dependent random variables
Let be a family of random independent k-element subsets of [n] = 1,2,...,n and let denote a family of ℓ-element subsets of [n] such that the event that S belongs to depends only on the edges of contained in S. Then, the edges of are ’weakly dependent’, say, the events that two given subsets S and T are in are independent for vast majority of pairs S and T. In the paper we present some results on the structure of weakly dependent families of subsets obtained in this way. We also list...
On Fibonacci numbers which are one more than a square.
On finite pattern-free sets of integers
On finite sequences satisfying linear recursions.
On Fleck quotients
On formulas for the Frobenius number of a numerical semigroup.
On Franel-Kluyver integrals of order three
On gaps in Rényi -expansions of unity for an algebraic number
Let be an algebraic number. We study the strings of zeros (“gaps”) in the Rényi -expansion of unity which controls the set of -integers. Using a version of Liouville’s inequality which extends Mahler’s and Güting’s approximation theorems, the strings of zeros in are shown to exhibit a “gappiness” asymptotically bounded above by , where is the Mahler measure of . The proof of this result provides in a natural way a new classification of algebraic numbers with classes called Q...
On Gauss sum characters of finite groups and generalized Bernoulli numbers