On the sum of squares of middle-third Cantor set

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.

References in corpus (1)

• Multiplication on uniform $\lambda$-Cantor sets