Abstract
Let $$\mathbb {N}$$ be the set of nonnegative integers. For a given set $$S\subset \mathbb {N}$$ the representation function $$R_S(n)$$ is defined as the number of solutions of the equation $$n=s+s', s<s', s,s'\in S$$ . In this paper, we characterize some sets which have the same representation functions.
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