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arXiv · 1810.08730

Digital images unveil geometric structures in pairs of relatively prime numbers

Benjamín A. Itzá-Ortiz·Roberto López-Hernández·Pedro Miramontes
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Abstract

We present a transformation, based on the B\'ezout'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.

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Benjamín A. Itzá-Ortiz, Roberto López-Hernández, Pedro Miramontes. 2018-10-20. Digital images unveil geometric structures in pairs of relatively prime numbers. https://doi.org/10.1007/s00283-019-09917-4

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