12.2.4 Modular Arithmetic
Chapter 9: Chapter 12 · MATHEMATICS-VOLUME 2 · EN medium
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. . Modular Arithmetic Having discussed the properties of operations like basic usual arithmetic operations, matrix addition and multiplication, join and meet of boolean matrices, one more new operation called the Modular Arithmetic is discussed in this section . The modular arithmetic refers to the process of dividing some number a by a positive integer n ( > ), called modulus, and then equating a with the remainder b modulo n and it is written as a ≡ (mod ) , read as ‘ a is congruent to b modulo n ’. Discrete Mathematics Here a ≡ (mod n ) means n k ⋅ for some integer k and b is the least non-negative integer when a is divided by n .
📖 Class 12 Mathematics English Volume 2 2025 Edition www.tntextbooks.in · Page 236
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. . Modular Arithmetic Having discussed the properties of operations like basic usual arithmetic operations, matrix addition and multiplication, join and meet of boolean matrices, one more new operation called the Modular Arithmetic is discussed in this section . The modular arithmetic refers to the process of dividing some number a by a positive integer n ( > ), called modulus, and then equating a with the remainder b modulo n and it is written as a ≡ (mod ) , read as ‘ a is congruent to b modulo n ’.
Discrete Mathematics Here a ≡ (mod n ) means n k ⋅ for some integer k and b is the least non-negative integer when a is divided by n . For instance, ≡ ≡− ≡ (mod ), (mod ) (mod ) and ≡ (mod ) , etc. Further the set of integers when divided by n , leaves the remainder , , , n - . In the case of , [ ]
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