Let a, b e Z where both a # 0 and b# 0. Now suppose that a = aid and b= bịd for a1, b1,d € Z. Prove that if d = gcd(a, b), then gcd(a1, b1) = 1.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .
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Let a, b e Z where both a # 0 and b# 0. Now suppose that a = aid and b=
bịd
for a1, b1,d € Z. Prove that if d = gcd(a, b), then gcd(a1, b1) = 1.
Transcribed Image Text:Let a, b e Z where both a # 0 and b# 0. Now suppose that a = aid and b= bịd for a1, b1,d € Z. Prove that if d = gcd(a, b), then gcd(a1, b1) = 1.
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