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Combinatorica

, Volume 20, Issue 4, pp 569–573 | Cite as

On a Conjecture of Kemnitz

  • Lajos Rónyai
Original Paper

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) = 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.

AMS Subject Classification (1991) Classes:  11B50, 11P21 

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Copyright information

© János Bolyai Mathematical Society, 2000

Authors and Affiliations

  • Lajos Rónyai
    • 1
  1. 1.Computer and Automation Institute, Hungarian Academy of Sciences; Budapest, Hungary; E-mail: lajos@nyest.ilab.sztaki.huHU

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