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exp^[1/2] mod p - tommy1729 - 12/07/2014

This is kinda a repost but I want to put attention to this again.

consider 2^x mod p

where x is a residue mod p for p an odd prime.

Now for some p we might define f(x) such that f(f(x)) = 2^x mod p.

Im very intrested in how many such p exist and how f behaves.


A naive argument exists that claims about 50% of the primes will do.
I assume this is wrong ?