Give an element of $ \mathbb{Z}[\sqrt{-17}] $ that is a product of two irreducibles and also a product of three irreducibles.
My thoughts so far:
Using the multiplicative norm $ N(a + b\sqrt{-17}) = a^2 + 17 b^2 $, we see that the units are precisely 1, -1. I can also see that there are no elements of norm $ 2,3,5,6,7,8,10,11,12,13,14,15... $. So if an element has norm 4 or 9 for example, then it is irreducible.
I don't really know where to go from here.
Any help appreciated. Thanks