  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 $aT_{x}+bT_{y}+cT_{z}$
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.
