Davenport constant with weights

Let A⊂{1,…,n−1}A⊂{1,…,n−1} and let (x1,…,xt)∈Zt(x1,…,xt)∈Zt be a sequence of integers with a maximal length such that for all (a1,…,at)∈At,∑1≤i≤taixi≢0(modn). The authors show that for any sequence of integers (x1,…,xn+t)∈Zn+t(x1,…,xn+t)∈Zn+t, there are b1,…,bn∈Ab1,…,bn∈A and 1≤k1