# A generalization of the Erdös-Surányi problem

Eiji Miyanohara

Research output: Contribution to journalArticle

### 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 Indagationes Mathematicae https://doi.org/10.1016/j.indag.2016.08.002 Accepted/In press - 2016 Jul 1

### Fingerprint

Integer
Roots of Unity
Odd
If and only if
Generalization

### 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)

### Cite this

A generalization of the Erdös-Surányi problem. / Miyanohara, Eiji.

In: Indagationes Mathematicae, 01.07.2016.

Research output: Contribution to journalArticle

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