Old and new necessary and sufficient conditions on in order that be a covering system
On a problem of P. Erdos and S. Stein
On a sum involving powers of reciprocals of an arithmetical progression.
On a variant of van der Waerden's theorem.
On a variation of the coin exchange problem for arithmetic progressions.
On arithmetic progressions having only few different prime factors in comparison with their length
On arithmetic progressions of equal lengthsand equal products of terms
On arithmetic progressions on Edwards curves
Let and a,q ∈ ℚ. Denote by the set of rational numbers d such that a, a + q, ..., a + (m-1)q form an arithmetic progression in the Edwards curve . We study the set and we parametrize it by the rational points of an algebraic curve.
On arithmetic progressions on elliptic curves.
On disjoint arithmetic progressions
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 generalised arithmetic and geometric progressions
On integers nonrepresentable by a generalized arithmetic progression.
On irregularities of sums of integers
On monochromatic subsets of a rectangular grid.
On Mycielski's problem on systems of arithmetical progressions
On Newman's conjecture and prime trees.
On non-intersecting arithmetic progressions
On non-intersecting arithmetic progressions
We improve known bounds for the maximum number of pairwise disjoint arithmetic progressions using distinct moduli less than x. We close the gap between upper and lower bounds even further under the assumption of a conjecture from combinatorics about Δ-systems (also known as sunflowers).
On perfect powers in products with terms from arithmetic progressions