Mathematics > Number Theory
[Submitted on 20 Oct 2018 (v1), last revised 2 Jul 2019 (this version, v2)]
Title:Digital images unveil geometric structures in pairs of relatively prime numbers
View PDFAbstract:We present a transformation, based on the Bézout's identity, which maps the set of pairs of relatively prime numbers $(p,q)$ with fixed $p$ and $0<q<p$, to pairs of relatively prime numbers in the $p\times p$ square in $\mathbb R^2$, in such a way that intriguing quadratic arcs show up. We exhibit parametrizations of quadratic curves which fit such quadratic arcs and we also justify algebraically the ensuing geometry.
Submission history
From: BenjamÃn A. Itzá-Ortiz [view email][v1] Sat, 20 Oct 2018 01:58:42 UTC (4,547 KB)
[v2] Tue, 2 Jul 2019 02:45:12 UTC (4,637 KB)
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