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This paper by Idaho University outlines influence of Egyptian and Eastern philosophies including Iranian Zoroastrian:
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The Medes Kingdom left a mark on Greek mythology. The Persian Empire, though, should not be equated with Zoroastrianism. It was an eastern religion, not even in Chaldea (Assyria and Babylon) It only took hold in Armenia and the Transcaucasus.
If the Zoroastrians did influence Greeks, it probably would have been in the time of Xerxes. The father of Democritus is said to have hosted Xerxes before Thermopylae. When Democritus used his inheritance money to travel east, he interacted with an elusive character named Ostanes. Ostanes is only recorded in Greek tradition, and later in Arabic tradition. He is not in any Persian sources. They say that he was a son of Darius I. He may have actually been the chief Magi at the time. He comes down as a later "Magician" in Greek sources, along with Hystaspes and Zoroaster. Hellenistic era writers used these pen names for various treatises on Astronomy and "magic". Pliny says that Ostanes invented "Magic", and taught it to all of the philosophers: Pythagoras, Empedocles, Democritus, Plato. While this is unlikely, you do have to wonder how the word magic came about. I wasn't going to answer this question, but I just happened to come across this stuff exactly when you asked it. Quite funny, given how unusual it is.