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arXiv · 1903.03392

Regular ternary triangular forms

Mingyu Kim·Byeong-Kweon Oh
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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 $aT_{x}+bT_{y}+cT_{z}$ 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.

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Mingyu Kim, Byeong-Kweon Oh. 2019-03-08. Regular ternary triangular forms. https://arxiv.org/abs/1903.03392

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