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**8**

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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 ...

**22**

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**5**answers

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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 ...

**12**

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**2**answers

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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 ...