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Formalized Mathematics

(a computer assisted approach)

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Volume 20, Issue 2 (Dec 2012)


Extended Euclidean Algorithm and CRT Algorithm

Hiroyuki Okazaki
  • Shinshu University, Nagano, Japan
/ Yosiki Aoki
  • Shinshu University, Nagano, Japan
/ Yasunari Shidama
  • Shinshu University, Nagano, Japan
Published Online: 2013-02-02 | DOI: https://doi.org/10.2478/v10037-012-0020-2


In this article we formalize some number theoretical algorithms, Euclidean Algorithm and Extended Euclidean Algorithm [9]. Besides the a gcd b, Extended Euclidean Algorithm can calculate a pair of two integers (x, y) that holds ax + by = a gcd b. In addition, we formalize an algorithm that can compute a solution of the Chinese remainder theorem by using Extended Euclidean Algorithm. Our aim is to support the implementation of number theoretic tools. Our formalization of those algorithms is based on the source code of the NZMATH, a number theory oriented calculation system developed by Tokyo Metropolitan University [8].

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About the article

This work was supported by JSPS KAKENHI 21240001 and 22300285

Published Online: 2013-02-02

Published in Print: 2012-12-01

Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-012-0020-2. Export Citation

This content is open access.

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