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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 314.10040

**Autor: ** Bovey, J.D.; Erdös, Paul; Niven, Ivan

**Title: ** Conditions for a zero sum modulo n. (In English)

**Source: ** Can. Math. Bull. 18, 27-29 (1975).

**Review: ** The authors use a theorem of *J. H. B. Kemperman* and *P. Scherk* [Canadian J. Math. 6, 238-252 (1954; Zbl 058.01901)] on the addition of residue classes (related to the well known Cauchy-Davenport theorem) to prove the following result. Let n > 0, k \geq 0, n-2k \geq 1. Then if a_{1}, ... ,a_{n-k} are any integers not more than n-2k of which lie in the same residue class (mod n), then there is a non-empty subset I of **{**1,2, ... ,n-k**}** such that **sum**_{i in I}a_{i} \equiv 0 (mod n). This result is best possible in the sense that if n \geq 3k-2 then the conclusion is not true if we allow n-2k+1 of the integers to lie in the same residue class.

**Reviewer: ** I.Anderson

**Classif.: ** * 11B13 Additive bases

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