# Trick(y) Question

Number Theory Level 5

Let $$\mathbb{Z}[\sqrt{5}i]$$ be the set of all complex numbers of the form $$z=a+b\sqrt{5}i$$, where $$a$$ and $$b$$ are integers. How many prime factors does the number 6 have in $$\mathbb{Z}[\sqrt{5}i]$$?

Did I mention that this is a trick question (or a tricky question, anyway)? Before answering, you may want to read up on "primes" and "irreducibles," taking note of the fact that the two concepts are not equivalent.

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