The stela of Dadusha of Eshnunna mentions the integration of the city of Burunda, the country of Eluhti, from the mountain of Diluba (probably a bad spelling of Luluban) to the mountain Lullum (country Lullubi) in his country of Warum.
Perhaps the country of Eluhti is that of Eluhhut of the archives of Mari. Indeed, a text by Ramman-Nirari I of Assyria mentions a campaign against the Kassites, the Kuti, the Lulumi and the Shubari. He declares to have eliminated his enemies from Lupdi to Rapiqum as far as Eluhat. This means that Eluhhut (Eluhat) was indeed a different city from that of Luluban or Ellipi (Lupdi), but on the former territory of the Lullubi. It is probable that the three cities are three extremities of the conquered territory.
However Eluhhut did not remain long under the dependence of Dadusha of Eshnunna since the texts of Mari mention Sarraya prince of Eluhhut, as well as Sukrum-Tessub king of Eluhhut. These nobles seem to defend other cities of the territory of Eluhhut, in relation with the Mariotes. Here are the texts and cities that seem to be of this region:
A.3024 reveals that when Sarraya were enthroned by Sarraya at Eluhhut by Zimri-Lim, Nahur and Burundu were towns that were placed under his responsibility.
XIII 144 refers to the obtaining of a pact of nonaggression between the people of Zalmaqum and Sarraya of Eluhhut, perhaps to allow battalions of warriors to pass through the territory of Eluhhut.
In XIV 94, Sarraya triumphed over 200 soldiers of Hursanum.
II 109 is a double letter of Sukrum-Tessub of Eluhhut defending his city of Amaz, and also the city of Azuhinum.
Some tablets evoke the work of wool, as on those of Nuzi. Moreover, these two sets of texts reveal the common cities of Nahur (Nasmur), Hurasina (Hursanum) and Burunda which is spelled Bur-Adawe. Karana is also mentioned nearby.
The geographical position of Eluhhut seems to me to be given by the more recent history of the region: in 638 AD, the Arabs ascended the course of the Diyala to encounter the Persians at Jalulah or Jalula. It is a city still existing in the present country of Iraq.
The positioning proposed here is based on the geographical likelihood given by the texts and the phonetic proximity of the name of the city. There is no archaeological excavation to support it.
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My notes of veracity :
Eluhhut is located near the present town of Jalula in Iraq: 3/5