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TANG, MIN
Bulletin of the Australian Mathematical Society, 06/2022, Letnik: 105, Številka: 3Journal Article
For a set A of positive integers and any positive integer n, let $R_{1}(A, n)$ , $R_{2}(A,n)$ and $R_{3}(A,n)$ denote the number of solutions of $a+a^{\prime }=n$ with $a, a^{\prime }\in A$ and the additional restriction that $a<a^{\prime }$ for $R_{2}$ and $a\leq a^{\prime }$ for $R_{3}$ . We consider Problem 6 of Erdős et al. ‘On additive properties of general sequences’, Discrete Math. 136 (1994), 75–99 about locally small and locally large values of $R_{1}, R_{2}$ and $R_{3}$ .
