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Let A, B be a pair of finite non-empty subsets of an abelian group G, such that |A + B| =|A| + |B|-1.Let c1, c2 be different elements in A + B having only one representation in A + B.Then one of the following two cases holds: (i).Let c1 =a1 +b1 and c2 =a2+b2, where a1 ∈ A and b1 ∈ B, then a1 =a2, or b1 =b2.