It would seem that the documentation to use depends on whether Argentina has signed an agreement of dual nationality with the country of residence of the traveler. There's no such agreement with Germany (only these countries: Chile, Colombia, Ecuador, El Salvador, Spain, United States (until 10/20/1981) Honduras, Italy, Nicaragua, Norway, Panama, and Sweden), so it looks like this would apply:
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Argentines who have been naturalized in countries with which the Argentine Republic has NOT signed a Dual Nationality Agreement.
They will be considered, for all purposes, as Argentines.
Entry:
a) In the case of presenting only a valid travel document of the acquired nationality, the same will be intervened or the pertinent card will be issued, stamping the entry stamp with the legend "ARGENTINE - 180 DAYS" handwritten under the stamp.
b) In the event that the Argentine condition is not stated in the foreign documentation and the entrant invokes it, he/she must prove this by presenting an Argentine Identity Document.
Exit:
To leave the country, they must do so with the pertinent Argentine documentation, unless the stay in the country has not exceeded the period of ONE HUNDRED AND EIGHTY (180) calendar days, this circumstance will allow them to leave with the travel document of their acquired nationality, which they have used to enter the country.
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Google-translated from
https://www.argentina.gob.ar/interior/migraciones/doble-nacionalidad