On the sum of squares of middle-third Cantor set

Published 14 Jan 2020 in math.DS and math.NT | (2001.04635v1)

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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