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In this paper, we study a combinatorial problem originating in the followingconjecture of Erdos and Lemke: given any sequence of n divisors of n,repetitions being allowed, there exists a subsequence the elements of which aresumming to n. This conjecture was proved by Kleitman and Lemke, who thenextended the original question to a problem on a zero-sum invariant in theframework of finite Abelian groups. Building among others on earlier works byAlon and Dubiner and by the author, our main theorem gives a new upper boundfor this invariant in the general case, and provides its right order ofmagnitude.

On a combinatorial problem of Erdos, Kleitman and Lemke