The given ring is "R=\\Z[\\sqrt{-2}]" .
Your question is wrong , Since we known that "R" is a Euclidean domain by defining a norm on "R" ,i,e,"N(a+b\\sqrt{-2})=a^2+2b^2" and every Euclidean domain is PID .
Again every PID is UFD.
Hence "R" is a UFD.
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