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For each positive integer m, let σA(n)=♯{(a,a′)∈A2:a+a′=n}, δA(n)=♯{(a,a′)∈A2:a−a′=n}, where n∈Zm and A is a subset of Zm. Recently Chen proved that for each positive integer m, there exists a set A⊆Zm such that A+A=Zm and σA(n)⩽288 for any n∈Zm. In this paper, the following results are proved: (i) for each positive integer m, there exists a set A⊆Zm such that Zm=A−A and δA(n)⩽7 for all n∈Zm with...
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