Partitions of nonnegative integers with identical representation functions

2022/08/16 by Cui-Fang Sun, Hao Pan, Sun, Cui-Fang +1
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Functional Equations Stability Results #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2208.07586

openalex publication_date 2022/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ℕ be the set of all nonnegative integers. For any integer r and m, let r+mℕ=\r+mk: k∈ℕ\. For S⊆ ℕ and n∈ ℕ, let R_S(n) denote the number of solutions of the equation n=s+s' with s, s'∈ S and s

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