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"Hindush (or Hindūš) was an Indian province of the Achaemenid Empire following the Achaemenid conquest of the Indus Valley circa 500 BC. According to Herodotus, it was the "easternmost province" of the empire. It is believed to have continued as a province until the invasion of the empire by Alexander the Great circa 326 BCE.".https://en.wikipedia.org/wiki/Hindush
The Greeks of Asia Minor, who were also part of the Achaemenid empire, called the province 'India'. More precisely, they called the people of the province as 'Indians' ('Ινδοι, Indoi) ['Ινδοι, Greek Word Study Tool, Tufts University]
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The name Hidūš (𐏃𐎡𐎯𐎢𐏁 in Old Persian cuneiform) as an Achaemenid territory in the DNa inscription of Darius the Great (c. 490 BCE).
Inscription DNa
The Persian king Darius the Great (r.521-486) was buried at Naqš-e Rustam, where he left two inscriptions.Livius.org
Source: Pierre Lecoq, Les inscriptions de la Perse achéménide (1997 Paris)
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Hindush among the Achaemenid satrapies on the Statue of Darius I.𓉔𓈖𓂧𓍯𓇌 H-n-d-wꜣ-y Hindush/India ("Arachosia, Sattagydia, and India are represented and named among the subject nations sculptured on the base of the Egyptian statue of Darius I from Susa."Yar-Shater, Ehsan (1982). Encyclopaedia Iranica. Routledge & Kegan Paul. p. 10.)
"Hindush (or Hindūš) was an Indian province of the Achaemenid Empire following the Achaemenid conquest of the Indus Valley circa 500 BC. According to Herodotus, it was the "easternmost province" of the empire. It is believed to have continued as a province until the invasion of the empire by Alexander the Great circa 326 BCE.".https://en.wikipedia.org/wiki/Hindush
The Greeks of Asia Minor, who were also part of the Achaemenid empire, called the province 'India'. More precisely, they called the people of the province as 'Indians' ('Ινδοι, Indoi) ['Ινδοι, Greek Word Study Tool, Tufts University]

The name Hidūš (𐏃𐎡𐎯𐎢𐏁 in Old Persian cuneiform) as an Achaemenid territory in the DNa inscription of Darius the Great (c. 490 BCE).
Inscription DNa
The Persian king Darius the Great (r.521-486) was buried at Naqš-e Rustam, where he left two inscriptions.Livius.org
Source: Pierre Lecoq, Les inscriptions de la Perse achéménide (1997 Paris)

- DNa, in the upper register, can be regarded as his political autobiography.
- Line 25 dâra \ Hiduš \ Sakâ \ haumavargâ \ Sa


Hindush among the Achaemenid satrapies on the Statue of Darius I.𓉔𓈖𓂧𓍯𓇌 H-n-d-wꜣ-y Hindush/India ("Arachosia, Sattagydia, and India are represented and named among the subject nations sculptured on the base of the Egyptian statue of Darius I from Susa."Yar-Shater, Ehsan (1982). Encyclopaedia Iranica. Routledge & Kegan Paul. p. 10.)