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ove or disprove: There exists an integer a such that 14 (3a-5) and 21 (2a +

ove or disprove: There exists an integer a such that 14 (3a-5) and 21 (2a +

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:** Prove or disprove: There exists an integer \( a \) such that \( 14 \mid (3a - 5) \) and \( 21 \mid (2a + 3) \). **Explanation:** The problem asks us to determine whether there is an integer value of \( a \) that satisfies both divisibility conditions simultaneously: 1. \( 14 \mid (3a - 5) \): This means \( 3a - 5 \) must be divisible by 14. 2. \( 21 \mid (2a + 3) \): This means \( 2a + 3 \) must be divisible by 21. We need to find such an integer \( a \), or prove that no such integer exists.
Transcribed Image Text:**Problem Statement:** Prove or disprove: There exists an integer \( a \) such that \( 14 \mid (3a - 5) \) and \( 21 \mid (2a + 3) \). **Explanation:** The problem asks us to determine whether there is an integer value of \( a \) that satisfies both divisibility conditions simultaneously: 1. \( 14 \mid (3a - 5) \): This means \( 3a - 5 \) must be divisible by 14. 2. \( 21 \mid (2a + 3) \): This means \( 2a + 3 \) must be divisible by 21. We need to find such an integer \( a \), or prove that no such integer exists.
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