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