Universal Sums of Triangular Numbers and Squares

2023/07/05 by Zichen Yang, Yang, Zichen
Mathematics · Physics and Astronomy · #11E25 #11F27 #11F30 #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2307.02118

openalex publication_date 2023/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study universal sums of triangular numbers and squares. Specifically, we prove that a sum of triangular numbers and squares is universal if and only if it represents 1,2,3,4,5,6,7,8,10,13,14,15,18,19,20,23,27,28,34,41,47, and 48.

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