Question 97
- Under what condition do there exist $n+1$ integers (not necessarily distinct) such that, for every choice of $n$ integers among the $n+1$, their sum is a power of $p$?
- Under what condition do there exist $n+1$ strictly positive integers (not necessarily distinct) such that, for every choice of $n$ integers among the $n+1$, their sum is a power of $p$?
- Under what condition do there exist $n+1$ strictly positive integers (not necessarily distinct) such that, for every choice of $n$ integers among the $n+1$, their sum is a power of $p$?