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Let a, b, n E Z. Prove: If a|n and b|n with gcd(a, b) = 1, then ab|n. (I

Let a, b, n E Z. Prove: If a|n and b|n with gcd(a, b) = 1, then ab|n. (I

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let \( a, b, n \in \mathbb{Z} \). Prove: If \( a \mid n \) and \( b \mid n \) with \(\gcd(a, b) = 1\), then \( ab \mid n \). (Lemma 1.1.17 might be useful)
Transcribed Image Text:Let \( a, b, n \in \mathbb{Z} \). Prove: If \( a \mid n \) and \( b \mid n \) with \(\gcd(a, b) = 1\), then \( ab \mid n \). (Lemma 1.1.17 might be useful)
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