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a) Show that the system of congruences.x: a2(modm1) and x

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 38E Chapter 4.SE

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 38E

a) Show that the system of congruences.x: ? a2(modm1) and x ? a2 (mod m2), where a1, a2. m1, and m2 are integers with m1 >0 and m2 > 0, has a solution if and only if gcd(m1, m2) | a1 – a2.________________b) Show that if the system in part (a) has a solution, then it is unique modulo 1cm(m1, m2).

Step-by-Step Solution:

Solution Step 1:In part (a) we have to show that system of congruences and Where are integers with and ,has a solution if and only if

Step 2 of 3

Chapter 4.SE, Problem 38E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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a) Show that the system of congruences.x: a2(modm1) and x