On the sum of squares of middle-third Cantor set

2020/01/14 by Zhiqiang Wang, Wang, Zhiqiang, Kan Jiang +5
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2001.04635

openalex publication_date 2020/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 answers a question posed by Athreya, Reznick,and Tyson.

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