On a combinatorial problem

What is it about?

In this paper some combinatorial problems are considered. The main result is the following. Let $A=(a_{ij})$ be a matrix of integers which has "sufficiently many'' rows and columns. Then for each integer $n$ there exist $k$ and $l$ such that $n$ divides $\sum^l_{i=k}\sum^l_{j=k}a_{ij}$. This result is generalized when $A$ is an $r$-dimensional array of integers. Another generalization is obtained when $A$ consists of real numbers and for each $\epsilon$, $\epsilon>0$, there exist $k$ and $l$ such that $|\sum^l_{i=k}\sum^l_{j=k}a_{ij}-\lfloor \sum^l_{i=k}\sum^l_{j=k}a_{ij}\rfloor|<\epsilon$. Reviewed by Slavcho Shtrakov

Featured Image