8. Let n and m be relatively prime integers and d e Z+. Prove the following statements. (a) If d (mn), then there exists positive integers d₁ and d2 such that d₁|n, d₁|m, and d = d₁d₂. (b) If d (mn), then d can be written in only one way as d = d₁d₂ where d₁ and d2 are positive divisors or n and m, respectively. (Hint: proof by contradiction.)

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ISBN:9780470458365
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8.
Let n and m be relatively prime integers and d e Z+. Prove the following statements.
d₁d₂.
=
(a) If d|(mn), then there exists positive integers d₁ and d₂ such that d₁|n, d₁|m, and d
(b) If d (mn), then d can be written in only one way as d = d₁d₂ where d₁ and d2 are positive divisors or n and
m, respectively. (Hint: proof by contradiction.)
Transcribed Image Text:8. Let n and m be relatively prime integers and d e Z+. Prove the following statements. d₁d₂. = (a) If d|(mn), then there exists positive integers d₁ and d₂ such that d₁|n, d₁|m, and d (b) If d (mn), then d can be written in only one way as d = d₁d₂ where d₁ and d2 are positive divisors or n and m, respectively. (Hint: proof by contradiction.)
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