We are interested in a sum-product type estimate. Let $p$ be an odd prime, and let $A$ be the order $p-1$ subgroup of $(\mathbb{Z}/p^2\mathbb{Z})^\times$. That is, let $A = \langle …

here is what I need to proof, have no idea were to start. I know there is some connection with the Stirling theorem. $$ \sum_{i=0}^{d}\binom{m}{i} \leq \left ( \frac{em}{d} \right …

I am an algebraist, and I am wondering if there is a definition for the following: Let $A_1$, $A_2$, $\ldots, A_n$ be sets of integers (or more generally, subsets of a group $G$). …

I have a question! Can someone explain how (the intuition, method?) one can try to construct an additive set of cardinality $N$ with a small sum set (around $N$) and a very large …

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 t …

I have a good motivation to ask the question below, but since the post is already a little long, and the problem looks rather natural and appealing (well, to me, at least), I'd rat …

Is it possible to find an approximate expression of $\frac{\sum_{i=1}^{n} k_i x_i}{\sum_{i=1}^{n} k_i}$ using $\langle k \rangle$, $\langle k^2 \rangle$, $\langle x \rangle$, and $ …

Since my original posting some ten days ago, I discovered an amazing example which changed significantly my perception of the problem. Accordingly, the whole post got re-written no …