Is it permissible for someone living in central Norway to fast Ramadan with Saudi Arabia, given that the days there are very long?

A Muslim must fast from the true dawn until sunset. If you begin and break your fast according to Saudi Arabia, this is not permissible and is considered intentionally breaking the fast during the daytime in Ramadan (definition). You must make up the days you fasted in this manner. However, if you mean fasting with Saudi Arabia at the beginning of the month based on moon sighting, this is a matter of scholarly disagreement, and the preponderant opinion is that the people of each country should follow their own sighting.