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- Title
Digital Images Unveil Geometric Structures in Pairs of Relatively Prime Numbers.
- Authors
Itzá-Ortiz, Benjamín A.; López-Hernández, Roberto; Miramontes, Pedro
- Abstract
In other words, we are proposing to highlight neighbors of the elements of the form I q i / I p i in the Farey sequence HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>F</mi><mi>p</mi></msub></math> ht . Hence HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msup><mi>d</mi><mn>2</mn></msup><mi>p</mi></mfrac><mo>=</mo><msup><mi>r</mi><mn>2</mn></msup><mi>w</mi></mrow></math> ht is an integer. Hence for HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>n</mi><mo> </mo><mi mathvariant="double-struck">Z</mi></mrow></math> ht , we get Indeed, when plotting the Bézout set HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="script">B</mi><mi>p</mi></msub></math> ht , we essentially are plotting points of the form.
- Subjects
PRIME numbers; EULER theorem; ARITHMETIC mean; DIGITAL images; QUADRATIC fields; QUADRATIC equations; EUCLIDEAN algorithm
- Publication
Mathematical Intelligencer, 2020, Vol 42, Issue 1, p30
- ISSN
0343-6993
- Publication type
Article
- DOI
10.1007/s00283-019-09917-4