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On rational points of orthogonal group

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arxiv 1409.5010 v1 pith:ZDA3VXWX submitted 2014-09-17 math.NT

Masanori Kobayashi , Chikara Nakayama This is my paper · ORCID
classification math.NT
keywords rationalintegervectorwhosebasisextendedgroupmembers
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abstract

Let $n$ be a positive integer. We show that a unit rational space vector whose multiple by $n$ is an integer vector can be extended to a rational orthonormal basis whose all members have the same property.

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  1. Extensions of integral orthoregular sets and icubes

    math.NT 2025-08 conditional novelty 8.0 of 10

    Every Gaussian-integer icube in dimension 4, and every one in dimension 3 whose norm is a sum of two squares, extends to an equal-length integral orthogonal basis; in dimension 4k+2 the norm must be a sum of two squares.

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