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#1 2010-04-23 06:59:14
- jaacob
- Member
- Registered: 2010-04-21
- Posts: 2
gcd & lcm
In ring R= Z + sqrt(-5)Z
1) do this elements 6 and 2(1+sqrt(-5)) have gcd? if yes, which is it
2) -------||--------------------------------------- lcm? ----||------
hint: use function N:Z+sqrt(-5)---->Z a+b*sqrt(-5) |-----> a^2+ 5* b^2
Is anybody wants to help..
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#2 2010-04-24 03:51:41
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: gcd & lcm
Hint:
Also, the function N, called the norm, has the very nice property that N(ab) = N(a)N(b). This is quite useful when talking about irreducibility.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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