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Find the gcd of 21-38i and 113-59¿ in two ways: first, by factorizing both numbers into Gaussian primes and, second, using the Euclidean algorithm. Show all work.

Find the gcd of 21-38i and 113-59¿ in two ways: first, by factorizing both numbers into Gaussian primes and, second, using the Euclidean algorithm. Show all work.

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. Find the gcd of 21–38i and 113–59¿ in two ways: first, by factorizing both numbers into Gaussian primes and, second, using the Euclidean algorithm. Show all work. b. Using Gaussian integers, find all representations of the number 9945 as a sum of two squares.
Transcribed Image Text:a. Find the gcd of 21–38i and 113–59¿ in two ways: first, by factorizing both numbers into Gaussian primes and, second, using the Euclidean algorithm. Show all work. b. Using Gaussian integers, find all representations of the number 9945 as a sum of two squares.
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