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3. Congruence Let a, b, c > 0, m 2 2 be integers. Prove that a = b (mod m) implies that ac = bc (mod mc).

3. Congruence Let a, b, c > 0, m 2 2 be integers. Prove that a = b (mod m) implies that ac = bc (mod mc).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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