Davenport constant with weights

Let [email protected]?{1,...,n-1} and let (x"1,...,x"t)@?Z^t be a sequence of integers with a maximal length such that for all (a"1,...,a"t)@?A^t,@?"1"@?"i"@?"ta"ix"[email protected]?0(modn). The authors show that for any sequence of integers (x"1,...,x"n"+"t)@?Z^n^+^t, there are b"1,...,b"[email protected]?A and [email protected]?k"1