Gauss first introduced the notion of congruence in Disquisitiones Arithmeticae (see Notes in Chapter 1). It is an extremely simple idea. Nevertheless, its importance and usefulness in number theory cannot be exaggerated.
This chapter is devoted to an exposition of the simplest properties of congruence. In Chapter 4, we shall go into the subject in more depth.
KeywordsChinese Remainder Theorem Congruence Class Principal Ideal Domain Congruence Modulo Arbitrary Commutative Ring
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