On a variant of the Erdös-Ginzburg-Ziv problem
by
Georges Grekos
Université de Saint-Etienne
Coauthors: Luis Gallardo (Université de Brest), Jukka Pihko (University of Helsinki)

This talk is about the content of a paper having the same title, which will appear in Acta Arithmetica. Let n, k be two integers, 0 < k < n+1. Denote by f(n, k) the smallest integer g such that any sequence of g integers belonging to exactly k classes modulo n, contains a subsequence of n terms having sum congruent to zero modulo n. In 1978, W. Brakemeier annouced [Monatshefte für Mathematik] results on f(n, k) for k > (n/2)+1. The proofs were given in his thesis [Braunschweig, 1973] and never published elsewhere. These results were not known to authors who published during the nineties and we rediscovered them, with proofs similar to those of W. Brakemeier, before rediscovering his original work.

Date received: March 18, 1999