On the sum of squares of the middle-third Cantor set

Zhiqiang Wang; Kan Jiang; Wenxia Li; Bing Zhao

doi:10.1016/j.jnt.2020.07.011

On the sum of squares of the middle-third Cantor set

Zhiqiang Wang, Kan Jiang, Wenxia Li, Bing Zhao

School of Mathematical Sciences

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

4 Scopus citations

Abstract

Let C be the middle-third Cantor set. In this paper, we show that for every x∈[0,4], there exist x₁,x₂,x₃,x₄∈C such that x=x₁²+x₂²+x₃²+x₄², which was conjectured in Athreya et al. (2019) [1].

Original language	English
Pages (from-to)	209-222
Number of pages	14
Journal	Journal of Number Theory
Volume	218
DOIs	https://doi.org/10.1016/j.jnt.2020.07.011
State	Published - Jan 2021

Keywords

Middle-[Formula presented] Cantor set
Middle-third Cantor set
Sum of four squares

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10.1016/j.jnt.2020.07.011

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title = "On the sum of squares of the middle-third Cantor set",

abstract = "Let C be the middle-third Cantor set. In this paper, we show that for every x∈[0,4], there exist x1,x2,x3,x4∈C such that x=x12+x22+x32+x42, which was conjectured in Athreya et al. (2019) [1].",

keywords = "Middle-[Formula presented] Cantor set, Middle-third Cantor set, Sum of four squares",

author = "Zhiqiang Wang and Kan Jiang and Wenxia Li and Bing Zhao",

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year = "2021",

month = jan,

doi = "10.1016/j.jnt.2020.07.011",

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AU - Wang, Zhiqiang

AU - Jiang, Kan

AU - Li, Wenxia

AU - Zhao, Bing

PY - 2021/1

Y1 - 2021/1

N2 - Let C be the middle-third Cantor set. In this paper, we show that for every x∈[0,4], there exist x1,x2,x3,x4∈C such that x=x12+x22+x32+x42, which was conjectured in Athreya et al. (2019) [1].

AB - Let C be the middle-third Cantor set. In this paper, we show that for every x∈[0,4], there exist x1,x2,x3,x4∈C such that x=x12+x22+x32+x42, which was conjectured in Athreya et al. (2019) [1].

KW - Middle-[Formula presented] Cantor set

KW - Middle-third Cantor set

KW - Sum of four squares

UR - https://www.scopus.com/pages/publications/85089492862

U2 - 10.1016/j.jnt.2020.07.011

DO - 10.1016/j.jnt.2020.07.011

M3 - 文章

AN - SCOPUS:85089492862

SN - 0022-314X

VL - 218

SP - 209

EP - 222

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

On the sum of squares of the middle-third Cantor set

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Keywords

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