Did Jesus meet the demoniacs in Gerasene or Gaderene?

Matt. 8:28, Mark 5:1-2, and Luke 8:26-27

Gadarenes (Matt. 8:28) - "And when He had come to the other side into the country of the Gadarenes, two men who were demon-possessed met Him as they were coming out of the tombs; they were so exceedingly violent that no one could pass by that road."
Gerasenes (Mark 5:1-2) - "And they came to the other side of the sea, into the country of the Gerasenes. 2And when He had come out of the boat, immediately a man from the tombs with an unclean spirit met Him,"
Gerasenes (Luke 8:26-27) - "And they sailed to the country of the Gerasenes, which is opposite Galilee. 27And when He had come out onto the land, He was met by a certain man from the city who was possessed with demons; and who had not put on any clothing for a long time, and was not living in a house, but in the tombs."

In Matthew it says "Gadarenes" while in Mark and Luke it says "Gerasenes." There are two possible explanations for the difference in spelling. First, there could be a minor scribal copying error on the spelling as there are different spellings in different manuscripts. Second, Gadara may have been the capital of the region in the Gerasenes and Matthew may have simply referred to it by a more local term: the Gaderenes.

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