Herodotus says that it was impossible to tell whether the influence of the Egyptians on the Ethiopians was stronger than that of the Ethiopians on the Egyptians.
What Herodotus and the Greeks referred to as Ethiopia was, in fact, the kingdom of Kush.

It was located up the Nile from Egypt.

As the Egyptian empire grew in strength and wealth, it strove to expand its power over its neighbors.

Egypt sent several military expeditions south along the Nile to try to conquer the black people of Kush.

They failed and the Kushites, in turn, endeavored to extend their power over Egypt.