On additive representation functions

Balasubramanian, R.; Giri, Sumit

doi:10.1142/s1793042115500633

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Cited by 3 publications

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“…Erdős et al [7,8] and Balasubramanian [1] studied the monotonicity properties of the functions R 1 (n), R 2 (n) and R 3 (n). For other related problems, see [2,3,12].…”

Section: Introductionmentioning

confidence: 99%

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On a Problem About Additive Representation Functions

Tang

2022

Bull. Aust. Math. Soc.

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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 $R_{3}$ .

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“…Erdős et al [7,8] and Balasubramanian [1] studied the monotonicity properties of the functions R 1 (n), R 2 (n) and R 3 (n). For other related problems, see [2,3,12].…”

Section: Introductionmentioning

confidence: 99%

“…For define the additive representation functions: In a series of papers [4, 5, 6], Erdős, Sárközy and Sós investigated the behaviour of these functions. Erdős et al [7, 8] and Balasubramanian [1] studied the monotonicity properties of the functions and For other related problems, see [2, 3, 12].…”

Section: Introductionmentioning

confidence: 99%