Thread: Quadratic primes

Question 1)
Prove that there are infinitely many prime in Q[sqrt(d)] .
Hint: It is almost identical to the proof that there are infinitely many prims in Z.

Question 2)
Find a prime factorization of 6 in Q[ sqrt(-1)] ?

Hi Perfecthacker,
Could you please teach me how to solve these questions? Thank you very much.

Question 2)
Find a prime factorization of 6 in Q[ sqrt(-1)] ?

We can non-trivally factor 6 as 2*3.
Now,
$\displaystyle 2=(1+i)(1-i)$
But three cannot be factored because it is not of the form 4k+1.
Thus,
$\displaystyle 6=3(1+i)(1-i)$