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Find the integer a such that a. a = -43 (mod23) and -22 ≤ a ≤ 0.

Find the integer a such that a. a = -43 (mod23) and -22 ≤ a ≤ 0.

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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**Find the integer \(a\) such that** \( a \equiv -43 \pmod{23} \) **and** \( -22 \leq a \leq 0 \). --- **Explanation:** This problem involves finding an integer \(a\) that satisfies two conditions: 1. \( a \equiv -43 \pmod{23} \): This means that when \(a\) is divided by 23, the remainder is the same as the remainder when \(-43\) is divided by 23. 2. \( -22 \leq a \leq 0 \): This sets the range within which \(a\) must fall, meaning \(a\) should be between \(-22\) and 0, inclusive. The goal is to find an integer \(a\) that meets both criteria.
Transcribed Image Text:**Find the integer \(a\) such that** \( a \equiv -43 \pmod{23} \) **and** \( -22 \leq a \leq 0 \). --- **Explanation:** This problem involves finding an integer \(a\) that satisfies two conditions: 1. \( a \equiv -43 \pmod{23} \): This means that when \(a\) is divided by 23, the remainder is the same as the remainder when \(-43\) is divided by 23. 2. \( -22 \leq a \leq 0 \): This sets the range within which \(a\) must fall, meaning \(a\) should be between \(-22\) and 0, inclusive. The goal is to find an integer \(a\) that meets both criteria.
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