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If a and b are integers, not both of which are zero, prove that gcd(2a - 3b, 4a -

Chapter 2, Problem 15

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QUESTION:

If a and b are integers, not both of which are zero, prove that gcd(2a - 3b, 4a - 5b) divides b; hence, gcd(2a + 3, 4a + 5) = 1.

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QUESTION:

If a and b are integers, not both of which are zero, prove that gcd(2a - 3b, 4a - 5b) divides b; hence, gcd(2a + 3, 4a + 5) = 1.

ANSWER:

Step 1 of 3

Given,

 divides any linear combination of  and .

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