## n

-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) = 4*n* - 3. In this note we prove that \(\) holds for every prime *p*. This implies that the value of *s*(*p*, 2) is either 4*p*-3 or 4*p*-2. For an arbitrary positive integer *n* it follows that \(\). The proof uses an algebraic approach.

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