JULIUS AFRICANUS
“The most famous exile that befell the Hebrews, then—to wit, when they were led captive by Nabuchodonosor king of Babylon—lasted 70 years, as Jeremias had prophesied. Berosus the Babylonian, moreover, makes mention of Nabuchodonosor. And after the 70 years of captivity, Cyrus became king of the Persians at the time of the 55th Olympiad, as may be ascertained from the Bibliothecæ of Diodorus and the histories of Thallus and Castor, and also from Polybius and Phlegon, and others besides these, who have made the Olympiads a subject of study. For the date is a matter of agreement among them all. And Cyrus then, in the first year of his reign, which was the first year of the 55th Olympiad, effected the first partial restoration of the people by the hand of Zorobabel, with whom also was Jesus the son of Josedec, since the period of 70 years was now fulfilled, as is narrated in Esdra the Hebrew historian. The narratives of the beginning of the sovereignty of Cyrus and the end of the captivity accordingly coincide. (Extant Fragments of the Five Books of the Chronography of Julius Africanus, chapter 13, 2.)
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It was 70 years of “captivity”. The captivity to Babylon ended as soon as Babylon had been defeated and Cyrus became king.
One could check whether a Tishri calendar or a Nisan calendar is intended and whether an accession-year system or a non-accession-year system was in mind. It should be possible to calculate the BCE date equivalent of Olympiad 55, year. The accepted starting point is 776 BCE for Olympiad 1, year 1.