From Dragon Quest Wiki
Quest #61 - "Mager Migraine"
Location Western Wormwood
Availability After doing Quest #039
Requested by Cephalgernon
Fulfilled to Cephalgernon
Item Required Hexite
Reward Lucida shard
Detail The Grand Wizard Cephalgernon in the well in Western Wormwood says he'll grant you a wish if you bring him some Hexite. Find and defeat Shogum in his Grotto lair to come up with the goods!
Hint for solution
Repeatable Yes