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Homer uses the terms Achaeans and Danaans (Δαναοί) as a generic term for Greeks in Iliad, and they were probably a part of the Mycenean civilization. The names Achaioi and Danaoi seem to be pre-Dorian belonging to the people who were overthrown. They were forced to the region that later bore the name Achaea after the Dorian invasion. In the 5th century BC, they were redefined as contemporary speakers of Aeolic Greek which was spoken mainly in Thessaly, Boeotia and Lesbos. There are many controversial theories on the origin of the Achaeans. According to one view, the Achaeans were one of the fair-headed tribes of upper Europe, who pressed down over the Alps during the early Iron age (1300 BC) to southern Europe. Another theory suggests that the Peloponnesian Dorians were the Achaeans. These theories are rejected by other scholars who, based on linguistic criteria, suggest that the Achaeans were mainland pre-Dorian Greeks. There is also the theory that there was an Achaean ethnos that migrated from Asia minor to lower Thessaly prior to 2000 BC. Some Hittite texts mention a nation lying to the west called Ahhiyava or Ahhiya. Egyptian documents refer to Ekwesh, one of the groups of sea peoples who attached Egypt during the reign of Merneptah (1213-1203 BCE), who may have been Achaeans.

What was redefined in the 5th century about the people of these names?
Answer: redefined as contemporary speakers of Aeolic Greek
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Towards the end of the Republic, religious and political offices became more closely intertwined; the office of pontifex maximus became a de facto consular prerogative. Augustus was personally vested with an extraordinary breadth of political, military and priestly powers; at first temporarily, then for his lifetime. He acquired or was granted an unprecedented number of Rome's major priesthoods, including that of pontifex maximus; as he invented none, he could claim them as traditional honours. His reforms were represented as adaptive, restorative and regulatory, rather than innovative; most notably his elevation (and membership) of the ancient Arvales, his timely promotion of the plebeian Compitalia shortly before his election and his patronage of the Vestals as a visible restoration of Roman morality. Augustus obtained the pax deorum, maintained it for the rest of his reign and adopted a successor to ensure its continuation. This remained a primary religious and social duty of emperors.

How many priesthoods was Augustus given?
Answer: unprecedented number
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The Hudson River flows through the Hudson Valley into New York Bay. Between New York City and Troy, New York, the river is an estuary. The Hudson River separates the city from the U.S. state of New Jersey. The East River—a tidal strait—flows from Long Island Sound and separates the Bronx and Manhattan from Long Island. The Harlem River, another tidal strait between the East and Hudson Rivers, separates most of Manhattan from the Bronx. The Bronx River, which flows through the Bronx and Westchester County, is the only entirely fresh water river in the city.

What river flows between the Hudson and East Rivers?
Answer:
Harlem River