On the sum of squares of middle-third Cantor set

Zhiqiang Wang; Kan Jiang; Wenxia Li; Bing Zhao

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arXiv · 2001.04635

On the sum of squares of middle-third Cantor set

Zhiqiang Wang·Kan Jiang·Wenxia Li·Bing Zhao

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Abstract

Let $C$ be the middle-third Cantor set. In this paper, we show that for every $x\in [0,4]$, there exist $x_1, x_2, x_3, x_4 \in C$ such that $$x= x_1^2+x_2^2+x_3^2+x_4^2,$$ which answers a question posed by Athreya, Reznick,and Tyson.

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BibTeX RIS

Zhiqiang Wang, Kan Jiang, Wenxia Li, Bing Zhao. 2020-01-14. On the sum of squares of middle-third Cantor set. https://arxiv.org/abs/2001.04635

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