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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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