Register to reply

Greatest Common Divisor in a strange extension ring.

by tomtom690
Tags: gcd, irreducible, prime, ring, z[sqrt(-5)]
Share this thread:
Dec14-10, 09:11 AM
P: 7
1. The problem statement, all variables and given/known data
I need to show that two elements in [tex]\textbf{Z}[/tex][[tex]\sqrt{-5}[/tex]] have gcd = 1.
The elements are 3 and 2+[tex]\sqrt{-5}[/tex]

2. Relevant equations

3. The attempt at a solution
My way of thinking was if I can show that both elements are irreducible, then they are both prime and hence have gcd of 1. I can show they are both irreducible, using the norm function - ie showing that if eg 3 = ab then either N(a) or N(b) is 1. This means that 3 is irreducible in this ring. I think.
Can somebody tell me if this is correct please? Like I said, I'm almost there, just need to polish it off!
Thanks in advance.
Phys.Org News Partner Science news on
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds

Register to reply

Related Discussions
Greatest common divisor Calculus & Beyond Homework 1
Greatest common divisor | Relatively prime Linear & Abstract Algebra 45
Greatest Common Divisor General Math 1
Greatest common divisor Calculus & Beyond Homework 24
Greatest common divisor Calculus & Beyond Homework 19