SOLVED: Exercise 12.3.6: Thcorem 12.3.5 states that the congruence modulo m rclation is an equivalence rclation (a) Why is 3 = 3 (mod 5)? Hint: Use the definition congruence modulo Prove that
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Define a binary operation * on the set A={1,2,3,4} as a*b=a b (mod 5). Show that 1 is the identity for * and all elements of the set A are invertible with2^(-1)=3 and 4^(-1)=4
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SOLVED: We can express modular arithmetic with the following equation: a = qm +r where dividend and 00 < a < 00 q = quotient and 0 < q < 0 mod
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3 Congruence
SOLVED: Definition 13 The sum of all elements, modulo m Em = C a (mod m) Definition 2 The sum of all invertible elements, modulo m = C (mod m) am Definition
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