Infinite sets of integers whose distinct elements do not sum to a power.
Infinitely often dense bases for the integers with a prescribed representation function.
Integer sets having the maximum number of distinct differences.
Konstruktion von nichtperiodischen Minimalbasen mit der Dichte ... für die Menge der nichtnegativen ganzen Zahlen.
Lower bounds for a conjecture of Erdős and Turán
We study representation functions of asymptotic additive bases and more general subsets of ℕ (sets with few nonrepresentable numbers). We prove that if ℕ∖(A+A) has sufficiently small upper density (as in the case of asymptotic bases) then there are infinitely many numbers with more than five representations in A+A, counting order.
Maximum line-free set geometry in .
Méthodes probabilistes en théorie des nombres
Minimal bases and powers of 2
Multiple set addition in .
Note on a result of Haddad and Helou.
Note on the Erdős-Graham theorem
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 a Problem Concerning Two Integer Sequences
On a problem of Frobenius.
On a question of additive number theory
On addition of two distinct sets of integers
What is the structure of a pair of finite integers sets A,B ⊂ ℤ with the small value of |A+B|? We answer this question for addition coefficient 3. The obtained theorem sharpens the corresponding results of G. Freiman.
On addition of two distinct sets of integers
On addition of two sets of integers
On additive bases
On additive bases