Mixed sums of triangular numbers and certain binary quadratic forms

2014/11/14 by Kazuhide Matsuda, Matsuda, Kazuhide
Mathematics · Physics and Astronomy · #11E25 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1411.5342

openalex publication_date 2014/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that for d=3,…,8, every natural number can be written as t_x+t_y+3t_z+dt_w, where x, y, z, and w are nonnegative integers and t_k=k(k+1)/2 (k=0,1,2,…) is a triangular number. Furthermore, we study mixed sums of triangular numbers and certain binary quadratic forms.

Citations

• On Certain Quaternary Quadratic Forms
• Mixed sums of squares and triangular numbers (III)

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