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Hi I have another problem..Two polynomials a(x) and b(x) are asociated iff a(x)|b(x) and b(x)|a(x)….Right? And now my problem..And polynomials are indivisible when gcd is asociated with 1..And there it is..In which universe is it for example 2??As I know 1 is indivisible by 2?Is there something I am overlooking? yes and all of this in any field e.g. $Z_3[x]$

Oh sorry I forget to specify which I am asking for:) So..I know that polynomials e.g. in $Z_3[x]$ are indivisible iff gcd is 1 or 2??And I am asking why?I know that 1 and 2 has to be mutually asociated..But I dont know why..I understand why these polynomials are indivisible, but I dont know why this asociation is valid..

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    So Am I right when would write this? $2=-1 $ hence $1/-1=-1=2 $all in $Z_3$.. but..there is another idea..Are these numbers asociated with 1 (neutral element), so the degree is not changing when I multiply?2011-01-09

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HINT $\rm\ \ gcd(2\:a,2\:b) = 2\ \iff\ gcd(a,b) = 1\ $ is true in every domain where $\:2 \ne 0$

The associates of $1$ are the units (invertibles). Therefore in any domain like $\rm\:\mathbb Z_3$ where $2$ is a unit, $\rm\ gcd(a,b)=2\ \iff\ gcd(a,b)=1\:$.