Show that if a, b, and m are integers such that m ≥ 2 and a ≡ b (mod m), then gcd(a, m) = gcd(b, m).

Solution :

Step 1 :

In this problem we have to prove that

Given that

Consider and

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Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.3 - Problem 50e

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Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.3 - Problem 50e

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

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Problem 50E

Show that if a, b, and m are integers such that m ≥ 2 and a ≡ b (mod m), then gcd(a, m) = gcd(b, m).

Step-by-Step Solution:
##### Textbook: Discrete Mathematics and Its Applications

##### Edition: 7

##### Author: Kenneth Rosen

##### ISBN: 9780073383095

Solution :

Step 1 :

In this problem we have to prove that

Given that

Consider and

Step 2 of 3
###### Chapter 4.3, Problem 50E is Solved

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Step 3 of 3

Since the solution to 50E from 4.3 chapter was answered, more than 310 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 50E from chapter: 4.3 was answered by , our top Math solution expert on 06/21/17, 07:45AM. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The answer to “Show that if a, b, and m are integers such that m ? 2 and a ? b (mod m), then gcd(a, m) = gcd(b, m).” is broken down into a number of easy to follow steps, and 26 words. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This full solution covers the following key subjects: gcd, mod, integers, show, such. This expansive textbook survival guide covers 101 chapters, and 4221 solutions.

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Show that if a, b, and m are integers such that m ? 2 and