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a) Show that if a and b are positive integers with a ? b,

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

Solution for problem 28E 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 28E

a) Show that if a and b are positive integers with a ≥ b, then gcd(a, b) = a if a = b, gcd(a,b) = 2 gcd(a/2, b/2) if a and b are even, gcd(a, b) = gcd(a/2, b) if a is even and b is odd. and gcd(a, b) = gcd(a – b, b) if both a and b are odd.

b)  Explain how to use (a) to construct an algorithm for computing the greatest common divisor of two positive integers that uses only comparisons, subtractions, and shifts of binary expansions, without using any divisions.

c)  Find gcd(1202. 4848) using this algorithm.

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Chapter 4.SE, Problem 28E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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a) Show that if a and b are positive integers with a ? b,

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