# Extended Euclidean Algorithm and CRT Algorithm

Hiroyuki Okazaki; Yosiki Aoki; Yasunari Shidama

Formalized Mathematics (2012)

- Volume: 20, Issue: 2, page 175-179
- ISSN: 1426-2630

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topHiroyuki Okazaki, Yosiki Aoki, and Yasunari Shidama. "Extended Euclidean Algorithm and CRT Algorithm." Formalized Mathematics 20.2 (2012): 175-179. <http://eudml.org/doc/268049>.

@article{HiroyukiOkazaki2012,

abstract = {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].},

author = {Hiroyuki Okazaki, Yosiki Aoki, Yasunari Shidama},

journal = {Formalized Mathematics},

language = {eng},

number = {2},

pages = {175-179},

title = {Extended Euclidean Algorithm and CRT Algorithm},

url = {http://eudml.org/doc/268049},

volume = {20},

year = {2012},

}

TY - JOUR

AU - Hiroyuki Okazaki

AU - Yosiki Aoki

AU - Yasunari Shidama

TI - Extended Euclidean Algorithm and CRT Algorithm

JO - Formalized Mathematics

PY - 2012

VL - 20

IS - 2

SP - 175

EP - 179

AB - 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].

LA - eng

UR - http://eudml.org/doc/268049

ER -

## References

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- [8] NZMATH development Group. http://tnt.math.se.tmu.ac.jp/nzmath/.
- [9] Donald E. Knuth. Art of Computer Programming. Volume 2: Seminumerical Algorithms, 3rd Edition, Addison-Wesley Professional, 1997. Zbl0895.68055
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