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Firepanda

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**[Number Theory] Find all the ideals with the element 6 in them in Z[√-5]**

Edited original question since I have now found the answer (I realize the title is inconsistent on the forum page), instead I am now trying to do part i) here

Is it possible to it this way:

Or is the structure of the question meaning my lecturer wants the actual ideals, and not just a general form? If so, how do i find which ideals contain 6.

I know the general form is

**a**=

**p**

^{a}

**q**

^{b}

**r**

^{c}

Whre a is an element of {0,1,2}, and b,c are an element of {0,1}

So there are 9 different combinations I think, do I have to check all 9? Or do all 9 have this property and there is no need to check?

Thanks

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