# On a problem of sidon in additive number theory, and on some related problems

```@article{Erds1941OnAP,
title={On a problem of sidon in additive number theory, and on some related problems},
author={Paul Erd{\"o}s and Paul Tur{\'a}n},
journal={Journal of The London Mathematical Society-second Series},
year={1941},
pages={212-215}
}```
• Published 1 October 1941
• Mathematics
• Journal of The London Mathematical Society-second Series
To the memory of S. Sidon. Let 0 < a, < a,. .. be an infinite sequence of positive integers. Denote by f(n) the number of solutions of n=a i +a;. About twenty years ago, SIDON 1) raised the question wether there exists a sequence a; satisfying f(n) > 0 for all n > 1 and lim f(n)'nE = 0 for all t > 0. In the present note, I will construct such a sequence. In fact, my sequence will satisfy (1) 0 < f(n) < c l log n for all n > l. (The c's will denote suitable positive absolute constants .) It…
308 Citations
A note on weak Sidon sequences
On A Problem of Erdos and Turn and Some Related Results
• Mathematics
• 1995
Abstract We employ the probabilistic method to prove a stronger version of a result of Helm, related to a conjecture of Erdős and Turan about additive bases of the positive integers. We show that for
Two Applications of Combinatorics to Number Theory
Let N denote the set of nonnegative integers, and let A be a subset of N. Let h 2 2. I f every sufficiently large integer can be written as the sum of h elements of A, with repetitions allowed, then
On the Erdös-Turán conjecture and related results
The Erdős-Turan Conjecture, posed in 1941 in [10], states that if a subset B of natural numbers is such that every positive integer n can be written as the sum of a bounded number of terms from B,
The Erdős–Turán property for a class of bases
• Mathematics
• 2004
An excellent account of this and related problems is given by Sárközy and Sós [11] (see also [3]). Not much is known about this famous conjecture. It can be easily shown that if a set of positive
On the size of finite Sidon sequences
Let h > 2 be -an integer. A set of positive integers B is called a Bh-sequence, or a Sidon sequence of order h, if all sums aI + a2 + * + ah, where ai E B (i = 1, 2, ..., h), are distinct up to