I have two questions:
1. Can someone show me how to apply the Euclidean algorithm to 2 and 1-3i in the integers of Q[Sqrt(-1)] ?
2. Assuming that Q[Sqrt(d)] is a Euclidean Field, and x,y are two quadratic integers in Q[Sqrt(d)] so that there exists a,b in Q[Sqrt(d)] so that x=a*y+g and Abs[N[g]] < Abs[N[y]]. How can we show that a,b are not necessarily unique?
Thank you! - Samson