Modular Arithmetic Pdf

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Modular Arithmetic Pdf

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Modular Arithmetic Practice Problems PDF

The central definition in studying modular arithmetic systems establishes a relationship between pairs of numbers with respect to a special number m called the modulus Definition 25 Two integers a and b are congruent modulo m if they di er by an integer multiple of m i e b a km for some k Z The study of the properties of the system of remainders is called modular arithmetic. It is an essential tool in number theory. 2.1. Definition of Z/nZ In this section we give a careful treatment of the system called the integers modulo (or mod) n. 2.1.1 Definition Let a, b.

CSCB109 Project Modular Arithmetic PDF

Modular Arithmetic PdfInverses in Modular arithmetic We have the following rules for modular arithmetic: Sum rule: IF a ≡ b(mod m) THEN a+c ≡ b+c(mod m). (3) Multiplication Rule: IF a ≡ b(mod m) and if c ≡ d(mod m) THEN ac ≡ bd(mod m). (4) Definition. Suppose that a mod m b mod m By the division theorem a mq a mod m and ms b mod m for some q s Z Then b mq a mod m ms b mod m m q s a mod m b mod m property Let a b m Z with m Then a b mod m 0 if and only if a mod m b mod m

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