Regular ternary triangular forms

2019/03/08 by Mingyu Kim, Byeong-Kweon Oh, Kim, Mingyu +1
Mathematics · #11E12 #11E20 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11E12 #msc:11E20

paper · pdf · doi:10.48550/arxiv.1903.03392

28 pages

arxiv created 2019/03/08 · openalex publication_date 2019/03/08 · arxiv updated 2019/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An integer of the form T_x=\fracx(x+1)2 for some positive integer x is called a triangular number. A ternary triangular form aT_x+bT_y+cT_z for positive integers a,b and c is called regular if it represents every positive integer that is locally represented. In this article, we prove that there are exactly 49 primitive regular ternary triangular forms.

Citations

• Almost universal ternary sums of triangular numbers

Related

• Regular triangular forms of rank exceeding 3
• Diagonal odd-regular ternary quadratic forms
• Regular ternary polygonal forms
• Ternary Sums of Squares and Triangular Numbers
• The representation of integers by positive ternary quadratic polynomials