Davenport constant with weights and some related questions, II

Let n ∈ N and let A ⊆ Z/nZ be such that A does not contain 0 and it is non–empty. Generalizing a well known constant, EA(n) is defined to be the least t ∈ N such that for all sequences (x1, . . . , xt) ∈ Z, there exist indices j1, . . . , jn ∈ N, 1 ≤ j1 < · · · < jn ≤ t, and (θ1, · · · ,θn) ∈ A with ∑n i=1 θixji ≡ 0 (mod n). Similarly, for any such set A, we define the Davenport Constant of Z/nZ with weight A denoted by DA(n) to be the least natural number k such that for any sequence (x1, · · · , xk) ∈ Z, there exists a non-empty subsequence {xj1 , · · · , xjl} and (a1, · · · al) ∈ A such that ∑l i=1 aixji ≡ 0 (mod n). In the present paper, in the special case where n = p is a prime, we determine the values of DA(p) and EA(p) where A is {1, 2, · · · , r} or the set of quadratic residues (mod p).