-1 integers there is a subsequence of length n whose sum is divisble by n. This result has led to several extensions and generalizations. A multi-dimensional problem from this line of research is the following. Let \(\) stand for the additive group of integers modulo n. Let s(n, d) denote the smallest integer s such that in any sequence of s elements from \(\) (the direct sum of d copies of \(\)) there is a subsequence of length n whose sum is 0 in \(\). Kemnitz conjectured that s(n, 2) = 4n - 3. In this note we prove that \(\) holds for every prime p. This implies that the value of s(p, 2) is either 4p-3 or 4p-2. For an arbitrary positive integer n it follows that \(\). The proof uses an algebraic approach.
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