### Abstract

Erdös-Surányi and Prielipp suggested to study the following problem: For any integers . k>0 and . n, are there an integer . N and a map . ε(lunate):(1,...,N)→(-1,1) such that . (0.1)n=∑j=1Nε(lunate)(j)jk? Mitek and Bleicher independently solved this problem affirmatively.In this paper we consider the case that for some positive odd integer . L the numbers . ε(lunate)(j) are . L-th roots of unity. We show that the answer to the corresponding question is negative if and only if . L is a prime power.

Original language | English |
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Journal | Indagationes Mathematicae |

DOIs | |

Publication status | Accepted/In press - 2016 Jul 1 |

### Keywords

- Prielipp's problem
- Representation of integers
- Signed sums
- The set of roots of unity
- Theorem of Erdös and Surányi

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Miyanohara, E. (Accepted/In press). A generalization of the Erdös-Surányi problem.

*Indagationes Mathematicae*. https://doi.org/10.1016/j.indag.2016.08.002