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Question on primes | Cypress Semiconductor

Question on primes

I found this interesting relationship

for n> a

mod(a^na, n) = a  ;only when n is a prime.

First of all is this true?  Does someone have a proof?

If this is true, is seems it may be an easy way to determine primes and might help in data encryptsion..

Also is this orginal or is it something already known?  When I was in high school I came up with a mathmatical proot for the Pythagorean theorem. I showed it to my math teacher and she came back the next day with a book showing this proof had been discovered hundreds of years before. Seeing that I was disappointed she said that just because someone else had discovered it first does meen I didn't also discover it. 

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