Part 2. Special Issues in Intellectual Systems Theory

On the progressive representation of periodic sets with restrictions on the beginning and the step

P. S. Dergach^a, D. E. Danilevskaya<sup>b

a</sup> Lomonosov Moscow State University
^b Tashkent Branch of Lomonosov Moscow State University

Abstract: In the article the set $K(n) := \mathbb {N} \setminus (n, n)$ is being examined, it’s presentation as union of as few arithmetic progressions as possible with constraints to the begining or step is being investigated. In both two cases appropriate accurate estimations have been found.

Keywords: arithmetic progression, natural series, minimization problem, types of constraints.