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.

**edit**

A naive argument exists that claims about 50% of the primes will do.

I assume this is wrong ?

**edit**

regards

tommy1729

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.

**edit**

A naive argument exists that claims about 50% of the primes will do.

I assume this is wrong ?

**edit**

regards

tommy1729