<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Linear Congruence Relation and Complete Residue Systems

Qingdao University of Science and Technology, China

Formalized Mathematics

{"article-title":"Linear Congruence Relation and Complete Residue Systems"}

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...

Linear Congruence Relation and Complete Residue Systems

Published Online: Jun 09, 2008

Page range: 181 - 187

DOI: https://doi.org/10.2478/v10037-007-0022-7

This content is open access.