MathDB

Let

(a_n)_{n=1}^\infty

be a sequence of real numbers. We say that the sequence

(a_n)_{n=1}^\infty

covers the set of positive integers if for any positive integer

m

there exists a positive integer

k

such that

\sum_{n=1}^\infty a_n^k=m

.
a) Does there exist a sequence of real positive numbers which covers the set of positive integers? b) Does there exist a sequence of real numbers which covers the set of positive integers?

Problem Statement