Linear Congruence Relation and Complete Residue Systems

Xiquan Liang; Li Yan; Junjie Zhao

Formalized Mathematics (2007)

  • Volume: 15, Issue: 4, page 181-187
  • ISSN: 1426-2630

Abstract

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In this paper, we defined the congruence relation and proved its fundamental properties on the base of some useful theorems. Then we proved the existence of solution and the number of incongruent solution to a linear congruence and the linear congruent equation class, in particular, we proved the Chinese Remainder Theorem. Finally, we defined the complete residue system and proved its fundamental properties.

How to cite

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Xiquan Liang, Li Yan, and Junjie Zhao. "Linear Congruence Relation and Complete Residue Systems." Formalized Mathematics 15.4 (2007): 181-187. <http://eudml.org/doc/267335>.

@article{XiquanLiang2007,
abstract = {In this paper, we defined the congruence relation and proved its fundamental properties on the base of some useful theorems. Then we proved the existence of solution and the number of incongruent solution to a linear congruence and the linear congruent equation class, in particular, we proved the Chinese Remainder Theorem. Finally, we defined the complete residue system and proved its fundamental properties.},
author = {Xiquan Liang, Li Yan, Junjie Zhao},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {181-187},
title = {Linear Congruence Relation and Complete Residue Systems},
url = {http://eudml.org/doc/267335},
volume = {15},
year = {2007},
}

TY - JOUR
AU - Xiquan Liang
AU - Li Yan
AU - Junjie Zhao
TI - Linear Congruence Relation and Complete Residue Systems
JO - Formalized Mathematics
PY - 2007
VL - 15
IS - 4
SP - 181
EP - 187
AB - In this paper, we defined the congruence relation and proved its fundamental properties on the base of some useful theorems. Then we proved the existence of solution and the number of incongruent solution to a linear congruence and the linear congruent equation class, in particular, we proved the Chinese Remainder Theorem. Finally, we defined the complete residue system and proved its fundamental properties.
LA - eng
UR - http://eudml.org/doc/267335
ER -

References

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