## 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 a1, ... ,an-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 sumi in Iai \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