Conjectures of Sun about sums of polygonal numbers

2021/09/30 by Kathrin Bringmann, Ben Kane, Bringmann, Kathrin +1
Mathematics · #11F11 #11F27 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2109.14793

openalex publication_date 2021/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that certain sums of generalized m-gonal numbers represent every positive integer if and only if they represent every positive integer up to an explicit bound C_m, verifying a conjecture of Sun for sufficiently large positive integers.

Citations

• A result similar to Lagrange's theorem

Related

• Universal sums of m-gonal numbers
• Fermat's polygonal number theorem for repeated generalized polygonal numbers
• Sums of four polygonal numbers: precise formulas
• Representations of integers as sums of four polygonal numbers and partial theta functions
• Sums of generalized polygonal numbers of almost prime "length"