On symmetric and antisymmetric balanced binary sequences.
On the additive completion of primes
On the concentration of points on modular hyperbolas and exponential curves
On the degree of regularity of generalized van der Waerden triples.
On the densities of sets of multiples.
On the Distribution of Prime Divisors on n. (Short Communication).
On the entry sum of cyclotomic arrays.
On the generalized Davenport constant and the Noether number
Known results on the generalized Davenport constant relating zero-sum sequences over a finite abelian group are extended for the generalized Noether number relating rings of polynomial invariants of an arbitrary finite group. An improved general upper degree bound for polynomial invariants of a non-cyclic finite group that cut out the zero vector is given.
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 density of sum-free sets
On the number of m-term zero-sum subsequences
On the number of prime factors of integers of the form ab + 1
On the number of subsets of relatively prime to and asymptotic estimates.
On the number of subsets relatively prime to an integer.
On the number of sums and products
On the number of ways of writing as a product of factorials.
On the possible orders of a basis for a finite cyclic group.
On the representation of integers as sums of distinct terms from a fixed set
On the representation of as .
Orthogonality and the maximum of Littlewood cosine polynomials