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Solve the congruence 15x - 5 = 8 (mod 52). If none exists, explain why. If there are one or more solutions, give a complete list of solution(s) modulo the modulus. = Solve the congruence 9x - 1 2 (mod 21). If none exists, explain why. If there are one or more solutions, give a complete list of solution(s) modulo the modulus.

Solve the congruence 15x - 5 = 8 (mod 52). If none exists, explain why. If there are one or more solutions, give a complete list of solution(s) modulo the modulus. = Solve the congruence 9x - 1 2 (mod 21). If none exists, explain why. If there are one or more solutions, give a complete list of solution(s) modulo the modulus.

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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**Learning Target N3:** I can correctly define the multiplicative inverse of an integer modulo m. I can determine the multiplicative inverse of an integer modulo m if it exists and correctly determine it if so. I can explain why an inverse doesn't exist if that is the case. I can use the inverse to solve linear congruences with zero, one, or many solutions. 1. Solve the congruence \(15x - 5 \equiv 8 \pmod{52}\). If none exists, explain why. If there are one or more solutions, give a complete list of solutions modulo the modulus. 2. Solve the congruence \(9x - 1 \equiv 2 \pmod{21}\). If none exists, explain why. If there are one or more solutions, give a complete list of solution(s) modulo the modulus.
Transcribed Image Text:**Learning Target N3:** I can correctly define the multiplicative inverse of an integer modulo m. I can determine the multiplicative inverse of an integer modulo m if it exists and correctly determine it if so. I can explain why an inverse doesn't exist if that is the case. I can use the inverse to solve linear congruences with zero, one, or many solutions. 1. Solve the congruence \(15x - 5 \equiv 8 \pmod{52}\). If none exists, explain why. If there are one or more solutions, give a complete list of solutions modulo the modulus. 2. Solve the congruence \(9x - 1 \equiv 2 \pmod{21}\). If none exists, explain why. If there are one or more solutions, give a complete list of solution(s) modulo the modulus.
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