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!