Erdös conjectured the existence of an infinite Sidon sequence of positive integers which is
an asymptotic basis of order 3. We progress towards this conjecture in several directions …

We prove that if $ A=\{a_1,\dots, a_ {| A|}\}\subset\{1, 2,\dots, n\} $ is a Sidon set so that $| A|=
n^{1/2}-L^\prime $, then $$ a_m= m\cdot n^{1/2}+\mathcal O\left (n^{7/8}\right)+\mathcal …

Let h, k≥ 2 be integers. We say a set A of positive integers is an asymptotic basis of order k
if every large enough positive integer can be represented as the sum of k terms from A. A set …

Abstract A set $ S\subset {\mathbb {N}} $ is a Sidon set if all pairwise sums $ s_1+ s_2 $(for
$ s_1, s_2\in S $, $ s_1\leqslant s_2 $) are distinct. A set $ S\subset {\mathbb {N}} $ is an …

Let h, k≥ 2 be integers. A set A of positive integers is called asymptotic basis of order k if
every large enough positive integer can be written as the sum of k terms from A. A set of …

A set $ S\subset\mathbb {N} $ is a Sidon set if all pairwise sums $ s_1+ s_2 $(for $ s_1,
s_2\in S $, $ s_1\leq s_2 $) are distinct. A set $ S\subset\mathbb {N} $ is an asymptotic basis …

Let k≥ 2 be an integer. We say a set A of positive integers is an asymptotic basis of order k if
every large enough positive integer can be represented as a sum of k terms from A. A set of …

Let h and k be positive integers. We say a set A of positive integers is an asymptotic basis of
order k if every large enough positive integer can be represented as the sum of k terms from …

Erd\" os conjectured the existence of an infinite Sidon sequence of positive integers which is
also an asymptotic basis of order 3. We make progress towards this conjecture in several …

Let k and l be positive integers satisfying. A set of positive integers is an asymptotic basis of
order k if every large enough positive integer can be represented as the sum of k terms from …