Regular ternary triangular forms

Abstract

An integer of the form T-x = x(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. (C) 2020 Elsevier Inc. All rights reserved.