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

Chapter 4, Problem 50E

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QUESTION:

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).

Questions & Answers

QUESTION:

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).

ANSWER:

Solution :

Step 1 :

In this problem we have to prove that

Given that

Consider  and

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