论文标题
三元算术，分解和班级第一问题
Ternary arithmetic, factorization, and the class number one problem
论文作者
论文摘要
自然数的普通二进制乘法可以通过考虑离散的晶格六边形量来以非平凡的方式推广到三元操作。通过此操作，定义了“ 3个primality”的自然概念 - 相对于三元乘法的原则 - 被定义，事实证明，几乎没有3个总数。它们对应于假想的二次字段$ \ mathbb {q}（\ sqrt { - n}）$，$ n> 0 $，带有奇数判别，其整数戒指承认了独特的因素化。我们还描述了如何确定数字作为三元产品的表示以及通常的原始测试和整数分解的相关算法。
Ordinary binary multiplication of natural numbers can be generalized in a non-trivial way to a ternary operation by considering discrete volumes of lattice hexagons. With this operation, a natural notion of `3-primality' -- primality with respect to ternary multiplication -- is defined, and it turns out that there are very few 3-primes. They correspond to imaginary quadratic fields $\mathbb{Q}(\sqrt{-n})$, $n>0$, with odd discriminant and whose ring of integers admits unique factorization. We also describe how to determine representations of numbers as ternary products and related algorithms for usual primality testing and integer factorization.
