Lughnasadh and Samhain -- coincidence?

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Until recently I knew nothing about Celtic Holidays but a chance occurence brought to my attention that 2 of the most important dates in Harry Potters Life are also important dates in Celtic Mythology. July 31 -- Harry's Birthday -- is the traditional beginning of Lughnasadh and of course October 31 -- date Voldemort killed his parents and tried to kill Harry -- corresponds to Samhain Coincidence? It is easy to find information on Samhain but harder to get complete information on Lughnasadh and the Celtic God "Lugh".