Question 1)

If alpha is a quadratic integers in Q[sqrt(-d)] , then define a notion of congruence (mod alpha).

Furthermore, define +, -, and X for congruence classes , and show that this notion is well-defined.

Question 2)

Prove that ( the integers of ) Q[sqrt(-5)] do not form a UFD.

Hint: Consider the quadratic integers that divide 6.

Please teach me how to solve these two questions. Thank you very much.