"I have often seen this gentlemen in Braunau and wonder if this means something," the Oberoesterreichische Nachrichten paper cited a local resident as saying on his Facebook page alongside a picture of the man it said resembled Hitler.
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Hitler was born in Braunau am Inn, then part of Austria-Hungary, in 1889.
Prosecutors confirmed the report.
The man, estimated to be 25 to 30 years old, was last seen in a local bookstore browsing through magazines about World War Two, adding he had identified himself in a local bar as "Harald Hitler.
On at least one occasion, he was photographed in front of the house where Hitler was born.
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Austria's parliament voted in December to buy the three-storey house where Hitler was born, which the government has rented since 1972 to control how it is used.
Glorifying Hitler or the Nazis is a crime in Austria, which Nazi Germany annexed in 1938.
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