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arXiv · 1201.5817

Some Connections Between The Arithmetic and The Geometry of Lipschitz Integers

António Machiavelo·Luís Roçadas
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Abstract

Some relationships between the arithmetic and the geometry of Lipschitz and Hurwitz integers are presented. In particular, it is shown that the (ternary) vector product of a Lipschitz integer $\alpha$ with two other Lipschitz integers, both orthogonal to $\alpha$, is a left and also a right multiple of $\alpha$, and that the vector product of two left multiples of $\alpha$ with any other Lipschitz integer is still a left multiple of $\alpha$. We also provide new arithmetical proofs for some old results of Gordon Pall, and raise a geometric problem on the location of some integral quaternions that is related to the factorization of some integers.

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António Machiavelo, Luís Roçadas. 2012-01-27. Some Connections Between The Arithmetic and The Geometry of Lipschitz Integers. https://arxiv.org/abs/1201.5817

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