4. Modular Inverse Compute an inverse of 70 modulo 39 by running the extended Euclidean algorithm and determining the Bézout coefficients.

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