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4) Consider the relatively prime pair of integers 123 and 14. a) (10 pts) Using the Euclidean Algorithm, find the Bézout Coefficients s, t such that 123 s + 14 t = 1 b) (10 pts) Use the previous result to solve the following linear congruence equation: 14 x = 64 (mod 123)

4) Consider the relatively prime pair of integers 123 and 14. a) (10 pts) Using the Euclidean Algorithm, find the Bézout Coefficients s, t such that 123 s + 14 t = 1 b) (10 pts) Use the previous result to solve the following linear congruence equation: 14 x = 64 (mod 123)

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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a) (123mod 19 ▪ 342 mod 19) mod 19 b) (12² mod 17)³ mod 13 2) (10 pts) Prove or disprove that for all integers a, b, and c, if alb and b/c then alc.
Transcribed Image Text:a) (123mod 19 ▪ 342 mod 19) mod 19 b) (12² mod 17)³ mod 13 2) (10 pts) Prove or disprove that for all integers a, b, and c, if alb and b/c then alc.
4) Consider the relatively prime pair of integers 123 and 14. a) (10 pts) Using the Euclidean Algorithm, find the Bézout Coefficients s, t such that 123 s + 14 t = 1 b) (10 pts) Use the previous result to solve the following linear congruence equation: 14 x = 64 (mod 123)
Transcribed Image Text:4) Consider the relatively prime pair of integers 123 and 14. a) (10 pts) Using the Euclidean Algorithm, find the Bézout Coefficients s, t such that 123 s + 14 t = 1 b) (10 pts) Use the previous result to solve the following linear congruence equation: 14 x = 64 (mod 123)
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