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**10**

votes

**2**answers

574 views

### Many representations as a sum of three squares

Let $r_3(n) = \left|\{(a,b,c)\in {\mathbb Z}^3 :\, a^2+b^2+c^2=n \}\right|$. I am looking for the maximum asymptotic size of $r_3(n)$. That is, the maximum number of representations that a number can ...

**8**

votes

**1**answer

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 ...

**22**

votes

**2**answers

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 $A\subset \mathbb{N}$ ...

**2**

votes

**3**answers

558 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} ...

**3**

votes

**0**answers

542 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 ...

**3**

votes

**1**answer

462 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 ...

**4**

votes

**1**answer

408 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 ...

**6**

votes

**2**answers

925 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 ...

**2**

votes

**2**answers

316 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 $d(P)$, ...

**11**

votes

**2**answers

735 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 < ...

**28**

votes

**3**answers

2k 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

**1**answer

639 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. ...

**7**

votes

**6**answers

3k 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 ...

**22**

votes

**5**answers

5k 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 ...