Hello All,

I have 2 questions regarding quadratic integers.

1a. Assume that

=

exists in Q[Sqrt(3)]. How can we show that if

__=__ that

__=__ ? Also, how can we show that if

__= __ ), then

=

? Lastly, if

__=__ , how can we show that

__= __ ?

I know that

is prime and that there are three congruence classes (mod

): one with -1, 0, and 1.

1b. How can it be proven that if

+

=

and x,y,z are quadratic integers in Q[Sqrt(-3)], then

(as described in 1a) must divide of one x, y, or z?

My first guess at this one is to reduce the equation to modulo

.

All help is appreciated!