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On zero-free subset sums. (English) Zbl 0863.11016

It is proved that when \(G\) is a finite group of prime order, any subset \(S\) of \(G\) such that \[ |S|\geq \sqrt {2} |G|^{1/2}+ 5\ln|G| \] contains a nonempty subset summing to zero. Asymptotically, this gives the tightest possible answer to a problem raised by Erdös and Heilbronn. A similar result is proved for general finite abelian groups.

MSC:

11B75 Other combinatorial number theory
20K01 Finite abelian groups
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