Question 31
Let $p$ be a given prime number. We call a set $A$ of positive integers a *p-set* if the cardinality of $A_p$, the set of residues of elements of $A$ modulo $p$, is $p-1$. Determine the smallest value of $n$ such that, for any *p-set* $A$ of $n$ elements, there exists a *p*-element subset of $A$ with sum divisible by $p$.
(Bayarmagnai G.)
(Bayarmagnai G.)