Kemnitz Conjecture [9] states that if we take a sequence of elements in $Z_{ p}^{ 2}$ of length $4p-3$, $p$ is a prime number, then it has a subsequence of length $p$, whose sum is $0$ modulo $p$. It is known that in $Z_{ p}^{ 3}$ to get a similar result we have to take a sequence of length atleast $9p-8$ . In this paper we will show that if we add a condition on the chosen sequence, then we can get a good upper and a lower bound for which similar results hold.
Categories: math.NT