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).
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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Theorem 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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