On a Conjecture of Kemnitz

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.

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Additional information

Received August 23, 1999

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Rónyai, L. On a Conjecture of Kemnitz. Combinatorica 20, 569–573 (2000). https://doi.org/10.1007/s004930070008

Download citation

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