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1. Div and Mod (a) Find the quotient ("div") and the remainder ("mod") when: (i) 23 is divided by 6 (ii) -42 is divided by 5 (b) Evaluate these quantities: (i) –101 mod 13 (ii) 199 mod 19 (c) to 4 modulo 12. List two negative integers and two positive integers that are congruent 2. Euclidean Algorithm Use the Euclidean algorithm to find ged(12345, 678). 3. Congruence Let a, b, c > 0, m 2 2 be integers. Prove that a = b (mod m) implies that ac = bc (mod mc). 4. Modular Inverse Compute an inverse of 70 modulo 39 by running the extended Euclidean algorithm and determining the Bézout coefficients.

1. Div and Mod (a) Find the quotient ("div") and the remainder ("mod") when: (i) 23 is divided by 6 (ii) -42 is divided by 5 (b) Evaluate these quantities: (i) –101 mod 13 (ii) 199 mod 19 (c) to 4 modulo 12. List two negative integers and two positive integers that are congruent 2. Euclidean Algorithm Use the Euclidean algorithm to find ged(12345, 678). 3. Congruence Let a, b, c > 0, m 2 2 be integers. Prove that a = b (mod m) implies that ac = bc (mod mc). 4. Modular Inverse Compute an inverse of 70 modulo 39 by running the extended Euclidean algorithm and determining the Bézout coefficients.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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1. Div and Mod (a) Find the quotient ("div") and the remainder ("mod") when: (i) 23 is divided by 6 (ii) -42 is divided by 5 (b) Evaluate these quantities: (i) –101 mod 13 (ii) 199 mod 19 (c) to 4 modulo 12. List two negative integers and two positive integers that are congruent 2. Euclidean Algorithm Use the Euclidean algorithm to find gcd(12345, 678). 3. Congruence Let a, b, c> 0, m > 2 be integers. Prove that a = b (mod m) implies that ac = bc (mod mc). 4. Modular Inverse Compute an inverse of 70 modulo 39 by running the extended Euclidean algorithm and determining the Bézout coefficients.
Transcribed Image Text:1. Div and Mod (a) Find the quotient ("div") and the remainder ("mod") when: (i) 23 is divided by 6 (ii) -42 is divided by 5 (b) Evaluate these quantities: (i) –101 mod 13 (ii) 199 mod 19 (c) to 4 modulo 12. List two negative integers and two positive integers that are congruent 2. Euclidean Algorithm Use the Euclidean algorithm to find gcd(12345, 678). 3. Congruence Let a, b, c> 0, m > 2 be integers. Prove that a = b (mod m) implies that ac = bc (mod mc). 4. Modular Inverse Compute an inverse of 70 modulo 39 by running the extended Euclidean algorithm and determining the Bézout coefficients.
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