Integer sequences avoiding prime pairwise sums.
Triangular numbers in geometric progression.
On and .
Sequences with bounded l.c.m. of each pair of terms
On addition of two sets of integers
On a problem of Sierpiński
On a conjecture of Sárközy and Szemerédi
Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers. In 1994, Sárközy and Szemerédi conjectured that there exist infinite additive complements A and B with lim sup A(x)B(x)/x ≤ 1 and A(x)B(x)-x = O(minA(x),B(x)), where A(x) and B(x) are the counting functions of A and B, respectively. We prove that, for infinite additive complements A and B, if lim sup A(x)B(x)/x ≤ 1, then, for any given M > 1,...
On the Siegel-Tatuzawa-Hoffstein theorem
On disjoint arithmetic progressions
On subset sums of a fixed set
Remarks on systems of congruence classes
On a question regarding visibility of lattice points, II
Prime values of reducible polynomials, I
Sequences with bounded l.c.m. of each pair of terms, III
A quantitative Erdös-Fuchs theorem and its generalization
A generalization of the classical circle problem
Sequences with bounded l.c.m. of each pair of terms II
Visibility of lattice points
A basis of ℤₘ, II
Given a set A ⊂ ℕ let denote the number of ordered pairs (a,a’) ∈ A × A such that a + a’ = n. Erdős and Turán conjectured that for any asymptotic basis A of ℕ, is unbounded. We show that the analogue of the Erdős-Turán conjecture does not hold in the abelian group (ℤₘ,+), namely, for any natural number m, there exists a set A ⊆ ℤₘ such that A + A = ℤₘ and for all n̅ ∈ ℤₘ.
On the average of the sum-of-a-divisors function
We prove an Ω result on the average of the sum of the divisors of n which are relatively coprime to any given integer a. This generalizes the earlier result for a prime proved by Adhikari, Coppola and Mukhopadhyay.
Page 1 Next