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Chapter 20
Modular Arithmetic
20.1 CLOCK ARITHMETIC
For addition, subtraction, and multiplication, the result of any of these
operations of two integers is also an integer. On the other hand, for a pair
of integers, the result of dividing one integer by the other is not necessarily
an integer. at is, the set of integers is closed under addition, subtrac-
tion, and multiplication, but not under division. However, any of the set
of rational numbers, the set of real numbers, and the set of complex num-
bers is closed under addition, subtraction, and multiplication, as well as
division (when dividing by any nonzero element).
For any nite set ...