Valentin Vornicu wrote:

Valentin Vornicu wrote:

Megus wrote:

Does it make any sense ?

No it doesn't. Let me tell you why: because $\mathbb{Z}[\sqrt 5]$ is not an UFD. For example $3\cdot 3 = 9 = (2-\sqrt 5 )(2+\sqrt 5) .$

Now why didn't anyone notice the HUGE abberation I have wrote above?

I ment $\mathbb{Z}[\sqrt{ - 5} ] = \mathbb{Z}[i\sqrt 5]$ is not an UFD (indeed $9\neq (2-\sqrt 5 ) (2 +\sqrt 5 ) = 4-5 = -1$

).

Actually both $\mathbb{Z}[\sqrt 5]$ and $\mathbb{Z}[\sqrt{11}]$ are Euclidean rings, thus UFDs also, so Megus' solution above is correct

Oh, good to hear that

- but that taught me one thing - next time I'll check whether the ring I use is UFD