I am reading Dummit and Foote Chapter 8, Section 8.1 - Euclidean DOmains

I am working through Example 2 on page 273 (see attachment)

Example 2 demonstrates that the quadratic integer ring is not a Euclidean domain.

I can follow the argument down to the point where D&F state (see attachment)

"Multiplying both sdes by would then imply that is a multiple of 3 in R, a contradiction"

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I cannot show this point - the mechanics of this fail me... can someone please help

Peter