A generalization of the Erdös-Surányi problem

Eiji Miyanohara

doi:10.1016/j.indag.2016.08.002

A generalization of the Erdös-Surányi problem

Eiji Miyanohara^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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

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title = "A generalization of the Erd{\"o}s-Sur{\'a}nyi problem",

abstract = "Erd{\"o}s-Sur{\'a}nyi 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.",

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author = "Eiji Miyanohara",

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language = "English",

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T1 - A generalization of the Erdös-Surányi problem

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PY - 2016/7/1

Y1 - 2016/7/1

N2 - 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.

AB - 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.

KW - Prielipp's problem

KW - Representation of integers

KW - Signed sums

KW - The set of roots of unity

KW - Theorem of Erdös and Surányi

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JF - Indagationes Mathematicae

ER -

A generalization of the Erdös-Surányi problem

Abstract

Keywords

ASJC Scopus subject areas

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