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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.r - Problem 10rq
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.r - Problem 10rq

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# a) How can you find a linear combination (with integer ISBN: 9780073383095 37

## Solution for problem 10RQ Chapter 4.R

Discrete Mathematics and Its Applications | 7th Edition

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Problem 10RQ

Problem 10RQ

a) How can you find a linear combination (with integer coefficients) of two integers that equals their greatest common divisor?

b) Express gcd(84. 119) as a linear combination of 84 and 119.

Step-by-Step Solution:
Step 1 of 3

Solution:

Step1

a) How can you find a linear combination (with integer coefficients) of two integers that equals their greatest common divisor?

A linear combination (with integer coefficients) of two integers that equals their greatest common divisor is found by Euclidean algorithm.

The Euclidean algorithm, is a productive technique for figuring the best regular divisor(GCD) of two numbers, the biggest number that partitions them two without leaving a remainder.It depends on the rule that the best normal divisor of two numbers does not change if the bigger number is supplanted by its distinction with the more modest number.

Step2

b) Express gcd(84. 119) as a linear combination of 84 and 119.

By using Euclidean algorithm     Therefore, gcd(84,119)=7

By going the inverse directions of the above divisions, we get = = = = So, Linear combination is Step 2 of 3

Step 3 of 3

##### ISBN: 9780073383095

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