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Hi,
you don't tell us if you have been member of an A-kasse (free student membership) during your study.
If not, then you must apply for membership at latest 2 weeks after graduation.
If you already are student member now, then you need to contact your A-kasse at latest 2 weeks after graduation and ask to have your status changed from student to graduate.
What is interesting for your will be if you are eligible for unemployment benefits ("dagpenge").
In other words if you meet the requirements for being eligble for benefits for graduates.
On of the requirements is that you were living in Denmark before you started your bachelor, and live in Denmark again no later than 14 days (including weekends) after you end your education.
So you must live in Denmark, but "permanent address" is not required. You can not get benefits from the Danish A-kasse, if you are not living in Denmark.
Another important thing, is that you must have right to work and live in Denmark. If you are an EU/EEA citizen then there is no problem. You have the right to live and work here.
If you are from a non EU/EEA country then you need work permit, before it is relevant to consider A-kasse.
For both EU or non-EU citizens you must also be able to meet the new residence requirement that came into force at January 1, 2019.
If you have not been free student member for at least 1 year, you must accept 1 month quarantine, where you don't get benefits. And because the payment will be for the last month, then you get your first payment after 2 months.
Best regards,
Anders, www.a-kasser.dk