m322qu1

m322qu1 - = a 2 b 2 We have proven that there is a...

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Spring 2009 Math 322 - Algebra II Quiz 1 - Greatest Common Divisor Look at the computation below, displaying the Euclidean algorithm in the principal ideal domain Z : 96 = 6 · 14 + 12 , | 12 | < | 14 | 14 = 1 · 12 + 2 , | 2 | < | 12 | ( 2 is the gcd of 96 and 12.) 12 = 6 · 2 + 0 Similarly, consider the Euclidean domain (hence a principal ideal domain) Z [ i ] = { a + bi : a, b Z } with the norm || a + bi ||
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Unformatted text preview: = a 2 + b 2 . We have proven that there is a Euclidean algorithm in Z [ i ] as above. In the near future we will prove that there is a gcd for any given pair of elements. Now, the question: Find the greatest common divisor of 3 + 5 i and 2 + 3 i in Z [ i ]. Ferit ¨ Ozt¨urk, Bo˘gazi¸ci University 2008...
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This note was uploaded on 05/04/2011 for the course MATH 321 taught by Professor Talinbudak during the Spring '11 term at BU.

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