Additive problem with $k$ numbers of a special form

A. A. Zhukova ; A. V. Shutov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part II, Tome 166 (2019), pp. 10-21.

Résumé

In this paper, we consider an additive problem of the form $n_1+n_2+\ldots+n_k=N$ with at least two summands, where the summands satisfy the condition $n_i\in\mathbb{N}(\alpha_i, I_i)$ for $1 \le i \le k$, where $\mathbb{N}(\alpha I)=\{n\in\mathbb{N}:\{n\alpha\}\in I\}$.

Détail

Keywords: additive problem, uniform distribution.

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