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24
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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 ...
22
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 ...
22
votes
2answers
1k 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
697 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 < ...
8
votes
1answer
2k views

What is the source of this E̶r̶d̶ő̶s̶ quote?

Namely, the following one "All problems appeared once in the [American Mathematical] Monthly." I remember reading it several years ago... When I first posed the question, I believed that I had ...
7
votes
6answers
2k views

If Erdős is published as Erdös in a paper, which do I cite?

There seems to be a few papers around with Erdős written as Erdös. For example: MR0987571 (90h:11090) Alladi, K.; Erdös, P.; Vaaler, J. D. Multiplicative functions and small divisors. II. J. Number ...
6
votes
2answers
837 views

Erdos distance problem n=12

The recent paper On the Erdos distinct distance problem in the plane Authors: Larry Guth, Nets Hawk Katz prodded me to get a non-trivial example. Here is what I cannot find: an example of 12 ...
4
votes
1answer
390 views

Degree reduction argument in Guth-Katz'sproof of Erdos distinct distance problem in the plane

In the middle of page 9 of http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.4105v1.pdf. They said " Now we select a random subset....choosing lines independently with probability $\frac{Q}{100}$. With ...
3
votes
1answer
624 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. ...
3
votes
1answer
453 views

A question about the number of intersections of lines in $R^{3}$

Suppose I have n lines in $R^{3}$ with the conditions that: no 3 lines in one plane, no 3 lines intersect at one point, for fixed 2 lines, no 3 lines intersect these 2 lines at the same time. what is ...
3
votes
0answers
496 views

Paul Erdős and Ramanujan Primes

It's easy to find Ramanujan's proof of Ramanujan primes: Ramanujan's Proof Wikipedia mentions that Paul Erdős also had a proof: Wikipedia article on Bertrand's Postulate Does anyone know the ...
2
votes
2answers
315 views

Determining the vector space for application of Cauchy Schwarz

In the paper "On the Erdős distinct distance problem in the plane" by Larry Guth and Nets Hawk Katz, http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.4105v1.pdf they define the functions $d(P)$, ...
2
votes
3answers
549 views

A limit from an Erdos paper

Hi, I need help to prove that, for $ N = \big\lfloor \frac{1}{2}n\log(n)+cn \big\rfloor $ with $c \in \mathbb R $ and $0 \leq k \leq n: $ $$ \lim_{n\rightarrow +\infty} \dbinom{n}{k} ...