# Proceedings of the 16th Conference on Computer Science and Intelligence Systems

## Combinatorial etude

### Miroslav Stoenchev, Venelin Todorov

Citation: Proceedings of the 16th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 25, pages 231234 ()

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Abstract. The purpose of this article is to consider a special class of combinatorial problems, the so called Prouhet-Tarry-Escot problem, solution of which is realized by constructing finite sequences of $\pm1$. For example, for fixed $p\in\NN$, is well known the existence of $n\_p\in\NN$ with the property: any set of $n\_p$ consecutive natural numbers can be divided into 2 sets, with equal sums of its $p^{{\scriptsize{\mbox{th}}}}$-powers. The considered property remains valid also for sets of finite arithmetic progressions of complex numbers.

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