Modular Congruence And Residue Classes Of Integers Modulo M:- Udeh Jisosdiebere

ABSTRACT ix In this work, we will only investigate the concept “Modular congruence and Residue Classes of Integers Modulo m”. Firstly we will define what Residue Class modulo m is and then establish the relationship between Residue class modulo m and congruence using division algorithm. We then prove the reflexivity, symmetric and transivity for a congruence relation to be an equivalence class (Residue Class). After then we would also establish a complete residue system which will give us a proper understanding of a residue classes modulo m. We will also perform addition and multiplication operation on residue classes modulo m and finally we will prove that the residue classes modulo m is an abelian group under addition operation.