Question 57
DB-B1. The source defines a power by $r=t^8$, $t\in\mathbb N$, $t\ge2$, $s\ge2$. Prove that for every $n\in\mathbb N$ there is $A\subseteq\mathbb N$ such that:
(1) $|A|=n$;
(2) for every $1\le k\le n$, the arithmetic mean of any $k$ elements of $A$ is also a power.
(1) $|A|=n$;
(2) for every $1\le k\le n$, the arithmetic mean of any $k$ elements of $A$ is also a power.