Side lengths of cubes with vertices in $\mathbb Z^n$

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Christian Bernert, Jens Reinhold
DOI: 10.48550/arxiv.2602.22202
Cited by: 0

Abstract

We determine the set of side lengths of $d$-dimensional cubes with vertices in $\mathbb Z^n$ using Witt's cancellation theorem from the algebraic theory of quadratic forms.

Fields of Study & Subjects

Algebraic Geometry and Number Theory Analytic Number Theory Research Advanced Combinatorial Mathematics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
25 February 2026
Language
EN
Document type
Preprint