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arXiv:2106.12019 [math.NT]AbstractReferencesReviewsResources

Length-Preserving Directions and Some Diophantine Equations

Juan Tolosa

Published 2021-06-22Version 1

We study directions along which the norms of vectors are preserved under a linear map. In particular, we find families of matrices for which these directions are determined by integer vectors. We consider the two-dimensional case in detail, and also discuss the extension to the three-dimensional case.

Comments: 5 figures
Journal: American Mathematical Monthly 128:2, 125-139, February 2021
Categories: math.NT, math.SP
Subjects: 15A18, 11D09, 15A06
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