Answered: Suppose a,b are nonzero integers. Then…

Suppose a,b are nonzero integers. Then gcd(a,b) = min{ma +nb : m,n ∈ Z and ma+nb > 0}. Furthermore, every common divisor of a,b is also a divisor of gcd(a,b).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.6: Congruence Classes

Problem 26E: Prove that a nonzero element in is a zero divisor if and only if and are not relatively prime.

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Suppose a,b are nonzero integers. Then gcd(a,b) = min{ma +nb : m,n ∈ Z and ma+nb > 0}. Furthermore, every common divisor of a,b is also a divisor of gcd(a,b).

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