# Tagged Questions

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### estimating binomial coefficients

There is a beautiful paper on the arXiv by Andrew Suk containing an asymptotic result about the Erdös-Szekeres convex polygon problem. I am struggling with one of the estimates he makes on page 4. He ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $A\subset \mathbb{N}$ ...
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### 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 ...
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### 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} \frac{\dbinom{\...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $d(P)$, (...