All Questions

The following question is motivated by pure curiosity; it is not a part of any research project and I do not have any applications. The question comes as an interpolation between two notoriously ...

Let $b \ge 1$ and $A\subseteq [0,b]$ be a set of integers (all intervals will be of integers). Write $hA := \underbrace{A + \ldots + A}_{h\text{ summands}} = \{ \sum_{i=1}^h a_i ~|~a_i \in A,\, \...

I'm being troubled by this problem on AoPS: https://artofproblemsolving.com/community/c6h1998237p13955033 I searched for any literature related to it such as Nguyen, Hoi H., and Van H. Vu., Squares ...

a) Let $S\subset \{1,2,\dotsc,N\}$ be a fairly thick set (with at least $N^{1-\epsilon}$ elements, say). Suppose that the intersection of, say, $$3 S - 3 S = \{a_1+a_2+a_3-(a_4+a_5+a_6): a_1,\dotsc,...

This is inspired by the recent question How many solutions $\pm1\pm2\pm3…\pm n=0$. The oeis entries A063865 linked to this question and A292476/A156700 for the related one "How many solutions $\pm1\...