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 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.
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 Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics 1(1):107-114 1990.
 Józef Białas. Some properties of the intervals. Formalized Mathematics 5(1):21-26 1996.
 Czesław Byliński. Functions and their basic properties. Formalized Mathematics 1(1):55-65 1990.