All Questions

R. Guy, Unsolved problems in number theory, 3rd edition, Springer, 2004. In this book, on page 167-168, Problem C5, Sums determining members of a set, discusses a question Leo Moser asked: suppose $X\...

There is a well-known theorem of Freiman saying that if $A$ is a finite set of integers with $|2A| \le 3|A|-4$, then $A$ is contained in an arithmetic progression with at most $|2A|-|A|+1$ terms. Is ...

It is a basic folklore fact from the area of additive combinatorics that a subset $A$ of an abelian group satisfies $|2A|<\frac32\,|A|$ if and only if $A$ is contained in a coset of a (finite) ...

The sumset of the subsets $A$ and $B$ of an additively written group is defined by $A+B:=\{a+b\colon a\in A,\ b\in B\}$. The basic idea to add sets has been around since Cauchy at least. Erdős and ...

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