Question 178
Given a prime number $p$ and an infinite set $A \subset \mathbb{Z}$. Show that one can always find a subset $B$ of $A$, $B$ contains $2p-2$ elements, and for any $p$ distinct elements of $B$, their arithmetic mean does not belong to $A$.
(Contributed by Fu Yunhao)
(Contributed by Fu Yunhao)