Regular ternary triangular forms

Abstract

An integer of the form $T_x=\frac{x(x+1)}{2}$ for some positive integer $x$ is called a triangular number. A ternary triangular form $a{T}_x+b{T}_y+c{T}_z$ 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.

28 pages