On Euclid's algorithm and elementary number theory

DOI10.1016/j.scico.2010.05.006zbMath1246.11187arXiv1506.05981OpenAlexW2145752266MaRDI QIDQ627201

João F. Ferreira, Roland C. Backhouse

Publication date: 21 February 2011

Published in: Science of Computer Programming (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.05981

zbMATH Keywords

greatest common divisorinvariantrational numberStern-Brocot treeenumeration algorithmalgorithm derivationcalculational methodEisenstein arrayEisenstein-Stern tree (aka Calkin-Wilf tree)Euclid's algorithm

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Related Items (5)

The analysis of mode-locking topology in an SIR epidemic dynamics model with impulsive vaccination control: infinite cascade of Stern-Brocot sum trees ⋮ A calculational approach to path-based properties of the Eisenstein-Stern and Stern-Brocot trees via matrix algebra ⋮ Cluster duality between Calkin-Wilf tree and Stern-Brocot tree ⋮ On Euclid's algorithm and elementary number theory ⋮ Complex mode-locking oscillations and Stern–Brocot derivation tree in a CSTR reaction with impulsive perturbations

Uses Software

• OEIS
• CalcCheck

Cites Work

• On Euclid's algorithm and elementary number theory
• On the shape of mathematical arguments
• Recounting the Rationals
• Recounting the Rationals: Twice!
• Guarded commands, nondeterminacy and formal derivation of programs
• FUNCTIONAL PEARL: Enumerating the rationals
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