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Use the Extended Euclidean Algorithm to find d = ged(85, 210) and write d as an integer combination of a = 85 and n = 210. (i) Use this to solve the following linear congruence. 85x 115 (mod 210). (ii) How many distinct solutions are there to 85.x = 115 in Z/210? List all the solutions, writing each as è where 0 ≤ c < 210.

Use the Extended Euclidean Algorithm to find d = ged(85, 210) and write d as an integer combination of a = 85 and n = 210. (i) Use this to solve the following linear congruence. 85x 115 (mod 210). (ii) How many distinct solutions are there to 85.x = 115 in Z/210? List all the solutions, writing each as è where 0 ≤ c < 210.

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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Use the Extended Euclidean Algorithm to find d = ged(85, 210) and write d as an integer combination of a = 85 and n = 210. (i) Use this to solve the following linear congruence. 85x 115 (mod 210). (ii) How many distinct solutions are there to 85.x = 115 in Z/210? List all the solutions, writing each as è where 0 ≤ c < 210.
Transcribed Image Text:Use the Extended Euclidean Algorithm to find d = ged(85, 210) and write d as an integer combination of a = 85 and n = 210. (i) Use this to solve the following linear congruence. 85x 115 (mod 210). (ii) How many distinct solutions are there to 85.x = 115 in Z/210? List all the solutions, writing each as è where 0 ≤ c < 210.
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