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 languageEnglish
    JournalIndagationes Mathematicae
    DOIs
    Publication statusAccepted/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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