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A Vermieterbescheinigung is a form of rent certificate that a tenant will receive from his/her landlord. According to the Federal Registration Act (Bundesmeldegesetz) a landlord has to provide a Vermieterbescheinigung within the first two weeks of a tenancy.
Moreover, the Vermieterbescheinigung is required for the registration at the Einwohnermeldeamt (local town hall), which is what you ought to do within the first two weeks of your move into a new place. In some cases, not registering your new address can lead to penalty fees.
I hope this was helpful. Please feel free to ask more questions if needed.