Sequences with bounded l.c.m. of each pair of terms
Sequences with bounded l.c.m. of each pair of terms II
Sequences with bounded l.c.m. of each pair of terms, III
Sets of integers and quasi-integers with pairwise common divisor
Sets of integers with pairwise common divisor and a factor from a specified set of primes
Sets with more sums than differences.
Short character sums with Fermat quotients
Slightly improved sum-product estimates in fields of prime order
Small maximal sum-free sets.
Small-sum pairs in abelian groups
Let be an abelian group and two subsets of equal size such that and both have size . Answering a question of Bihani and Jin, we prove that if is aperiodic or if there exist elements and such that has a unique expression as an element of and has a unique expression as an element of , then is a translate of . We also give an explicit description of the various counterexamples which arise when neither condition holds.
Solving a linear equation in a set of integers I
Solving a linear equation in a set of integers II
Some additive and multiplicative problem sin number theory
Some additive applications of the isoperimetric approach
Let be a group and let be a finite subset. The isoperimetric method investigates the objective function , defined on the subsets with and , where is the product of by .In this paper we present all the basic facts about the isoperimetric method. We improve some of our previous results and obtain generalizations and short proofs for several known results. We also give some new applications.Some of the results obtained here will be used in coming papers to improve Kempermann structure...
Some classes of numbers and derivatives.
Some explicit constructions of sets with more sums than differences
Some problems of combinatorial number theory related to Bertrand's postulate.
Some properties of the multiple binomial transform and the Hankel transform of shifted sequences.
Some results in additive number theory I: The critical pair theory
Some solved and unsolved problems in combinatorial number theory, ii
In an earlier paper [9], the authors discussed some solved and unsolved problems in combinatorial number theory. First we will give an update of some of these problems. In the remaining part of this paper we will discuss some further problems of the two authors.