Weighted sums of generalized polygonal numbers with coefficients 1 or 2

2020/06/08 by Daejun Kim, Kim, Daejun
Mathematics · #11E08 #11E12 #11E25 #Advanced Mathematical Identities #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2006.04490

openalex publication_date 2020/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we consider weighted sums of generalized polygonal numbers with coefficients 1 or 2. We show that for any m≥10, those weighted sums of generalized m-gonal numbers represent every non-negative integers if they only represent 1, m-4, and m-2. Furthermore, we study representations of sums of four generalized polygonal numbers with coefficients 1 or 2.

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