Question 88
A set $E$ of strictly positive integers is called interesting if for every $n \geqslant 1$ and for all pairwise distinct elements $x_{1}, \ldots, x_{n}$ of $E$, their arithmetic mean $\frac{1}{n}\left(x_{1}+\ldots+x_{n}\right)$ and their geometric mean $\left(x_{1} \cdot \ldots \cdot x_{n}\right)^{\frac{1}{n}}$ are integers.
1. Does there exist an interesting set $E$ containing exactly 2022 elements?
2. Does there exist an infinite interesting set $E$?
1. Does there exist an interesting set $E$ containing exactly 2022 elements?
2. Does there exist an infinite interesting set $E$?