A generalization of a classical zero-sum problem

Abstract

In this note, we supply the details of the proof of the fact that if a 1 , … , a n + Ω ( n ) are integers, then there exists a subset M ⊂ { 1 , … , n + Ω ( n ) } of cardinality n such that the equation ∑ i ∈ M a i x i ≡ 0 ( mod n ) admits a solution ( x i ) i ∈ M ∈ ( U ( Z / n Z ) ) n , where U ( Z / n Z ) stands for the multiplicative group modulo n.