Darius the Mede Cyrus the Great -co-rule- (oct 7, 539 BC – jan 1, 536 BC)

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After Babylon fell to Cyrus (at the head of the Army), Cyrus made placed his uncle Darius-the-Mede "as King" over Babylon (Dan 9/1) while Cyrus stayed at the head of the Army.
After annexing the rest of the empire by 536 BC, Cyrus returned as sole Rex over the expanded Empire and as Suzerain over the Jews.
536 BC is hence the date intended by scriptures as "the first year of Cyrus"

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