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Assume that a b•c and that gcf(a,b) = 1. Prove that a lc (hint: use the result that gcf(a,b) = 1 iff there exist x,yeZ such that ax+b y 1)

Assume that a b•c and that gcf(a,b) = 1. Prove that a lc (hint: use the result that gcf(a,b) = 1 iff there exist x,yeZ such that ax+b y 1)

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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**Problem Statement:** Assume that \( a \mid b \cdot c \) and that \(\text{gcf}(a,b) = 1\). Prove that \( a \mid c \). **Hint:** Use the result that \(\text{gcf}(a,b) = 1\) if and only if there exist \( x, y \in \mathbb{Z} \) such that \( a \cdot x + b \cdot y = 1 \).
Transcribed Image Text:**Problem Statement:** Assume that \( a \mid b \cdot c \) and that \(\text{gcf}(a,b) = 1\). Prove that \( a \mid c \). **Hint:** Use the result that \(\text{gcf}(a,b) = 1\) if and only if there exist \( x, y \in \mathbb{Z} \) such that \( a \cdot x + b \cdot y = 1 \).
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