MathDB

Let

0<a_k<1

for

k=1,2,... .

Give a necessary and sufficient condition for the existence, for every

0<x<1

, of a permutation

\pi_x

of the positive integers such that

x= \sum_{k=1}^{\infty} \frac{a_{\pi_x}(k)}{2^k}.

P. Erdos

Problem Statement