TITLE: Two Equal Series?
QUESTION [5 upvotes]: Hey all,
I'd like to know if anyone has a link to a proof of the following?
Take two infinite sequences $a_n$ and $b_n$ such that
$$\sum_{n=1}^\infty a_n^s=\sum_{n=1}^\infty b_n^s=finite$$
for all $s\in\mathbb{N}$. Then, after some rearrangement, $a_i=b_i$ for all i? I have my own proof which I am pretty sure is correct and I'd very much like to know if such a proof has been given before (to see if it is any different)
Thanks in advanced for any help :)

REPLY [6 votes]: Here is a link to a counterexample for conditionally convergent complex series.