On Euclid’s algorithm and elementary number theory

On Euclid’s algorithm and elementary number theory

Algorithms can be used to prove and to discover new theorems. This paper shows how algorithmic skills in general, and the notion of invariance in particular, can be used to derive many results from Euclid’s algorithm. We illustrate how to use the algorithm as a verification interface (i.e., how to v...

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Bibliographic Details
Main Authors: Backhouse, Roland, Ferreira, João F.
Format: Article
Published: Elsevier B.V. 2011
Subjects:
Number theory; Calculational method; Greatest common divisor; Euclid’s algorithm; Invariant; Eisenstein array; Eisenstein–Stern tree (aka Calkin–Wilf tree); Stern–Brocot tree; Algorithm derivation; Enumeration algorithm; Rational number
Online Access:https://eprints.nottingham.ac.uk/1856/

Internet

https://eprints.nottingham.ac.uk/1856/

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