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
On properties of systems of arithmetic sequences
On rainbow arithmetic progressions.
On sets of integers containing k elements in arithmetic progression
On simultaneous arithmetic progressions on elliptic curves.
On Squarefree Numbers in Arithmetic Progressions.
On the critical pair theory in ℤ/pℤ
On the discrepancy of quasi-progressions.
On the greatest prime factor of an arithmetical progression. II
On the growth of a van der Waerden-like function.
On the lonely runner conjecture
Suppose runners having nonzero distinct constant speeds run laps on a unit-length circular track. The Lonely Runner Conjecture states that there is a time at which a given runner is at distance at least from all the others. The conjecture has been already settled up to seven () runners while it is open for eight or more runners. In this paper the conjecture has been verified for four or more runners having some particular speeds using elementary tools.
On the Maximal Length of Two Sequences of Integers in Arithmetic Progressions with the Same Prime Divisors.