Proof that Z[(1+sqrt(-19))/2] is not a Euclidean domain

This is an example of a ring which is a PID but is not a Euclidean domain.

[juliefinkjulesheartmagic]

Thank you for the awesome video! You’re so calm and clear.

[bjorncarlsson]

Slightly over my head but fascinating! Quadratic integers are intruiging. One would get the same result for Z[(1+√-43)/2]? And for some reason Z[√-13] is neither eucludian or a UFD.