On the sum of squares of middle-third Cantor set

Zhiqiang Wang, Kan Jiang, Wenxia Li +1

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 a…