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Show that if n divides m where m and n are positive integers greater than 1, then a = b (mod m) implies a = b (mod n) for any positive integers a and b. Show that a c = b.c (mod m) with a, b, c and m integers with m≥2 does not imply a = b (mod m). Using the Euclidean Algorithm, find gcd(3084, 1424). Show your working.

Show that if n divides m where m and n are positive integers greater than 1, then a = b (mod m) implies a = b (mod n) for any positive integers a and b. Show that a c = b.c (mod m) with a, b, c and m integers with m≥2 does not imply a = b (mod m). Using the Euclidean Algorithm, find gcd(3084, 1424). Show your working.

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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1. (a) Show that if n divides m where m and n are positive integers greater than 1, then a = b (mod m) implies a = b (mod n) for any positive integers a and b. (b) Show that a·c = b⋅c (mod m) with a, b, c and m integers with m≥2 does not imply a = b (mod m). (c) Using the Euclidean Algorithm, find gcd(3084, 1424). Show your working.
Transcribed Image Text:1. (a) Show that if n divides m where m and n are positive integers greater than 1, then a = b (mod m) implies a = b (mod n) for any positive integers a and b. (b) Show that a·c = b⋅c (mod m) with a, b, c and m integers with m≥2 does not imply a = b (mod m). (c) Using the Euclidean Algorithm, find gcd(3084, 1424). Show your working.
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