All Questions

I would like to know whether the problem described below has appeared in the literature and/or whether similar questions have been studied. I would be very happy to find some references or, if none ...

In the course of some recent research, I've sketched out a proof of the following result. My basis question is: is the result interesting? Proposition There exists an absolute constant $c$ such ...

Let $p$ be a prime, let $A$ be a subset of $\mathbb{F}_p$, and let $v \in \mathbb{F}_p \setminus \{0\}$. Under what conditions is $|v \cdot A + A|$ (that is, $|\{ va + b : a \in A,\ b \in A \}|$) ...

We consider a group finite $G$. We say a set $A\subset G$ injects a set $B$ if $|A+B| = |A||B|$, and let $I(B) = \max \{|A| :A\text{ injects } B\}$. For a subgroup $H$, it is well-known that $I(H) = |...

Suppose $G$ is a group, $S \subset G$. Let’s call $S$ a Sidon subset iff $\forall$ quadruples $(a, b, c, d)$ of distinct elements of $S$ we have $ab \neq cd$ (named after Simon Sidon who studied such ...

Let $k<N$ and $P_1, ..., P_{2k+1}, \lambda_1, ..., \lambda_k$ be elements of a finite group $G$ of size $N$. Find the minimum number of solution of the system $$P_{2i} + P_{2i+1} = \lambda_i, \...