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.
@article{bwmeta1.element.doi-10_2478_v10037-007-0022-7,
author = {Xiquan Liang and Li Yan and Junjie Zhao},
title = {Linear Congruence Relation and Complete Residue Systems},
journal = {Formalized Mathematics},
volume = {15},
year = {2007},
pages = {181-187},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-007-0022-7}
}
Xiquan Liang; Li Yan; Junjie Zhao. Linear Congruence Relation and Complete Residue Systems. Formalized Mathematics, Tome 15 (2007) pp. 181-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-007-0022-7/
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