21
votes
2answers
958 views

The Erdős-Turán conjecture or the Erdős' conjecture?

This has been bothering me for a while, and I can't seem to find any definitive answer. The following conjecture is well known in additive combinatorics: Conjecture: If $A\subset \mathbb{N}$ ...
11
votes
2answers
686 views

Did Erdős publish his proof of the multiplicative version of the Erdős-Turán conjecture?

I read in an article of Erdős ("Extremal problems in number theory") that he had a proof of the multiplicative version of the Erdős-Turán conjecture. The statement of this theorem is Let $a_1 < ...
24
votes
3answers
1k views

Does there exist a comprehensive compilation of Erdos's open problems?

Fan Chung and Ron Graham's book Erdos on Graphs: His Legacy of Unsolved Problems (A. K. Peters, 1998) collects together all of Erdos's open problems in graph theory that they could find into a single ...
3
votes
1answer
621 views

A limit involving the totient function

P. Erdős and Leon Alaoglu proved in [1] that for every $\epsilon > 0$ the inequality $\phi(\sigma(n)) < \epsilon \cdot n$ holds for every $n \in \mathbb{N}$, except for a set of density $0$. C. ...
21
votes
5answers
4k views

Erdos Conjecture on arithmetic progressions

Introduction: Let A be a subset of the naturals such that $\sum_{n\in A}\frac{1}{n}=\infty$. The Erdos Conjecture states that A must have arithmetic progressions of arbitrary length. Question: I ...