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Let p be a prime larger than 100.
Let 0 < n < p.

How many residue classes does 2^^n mod p have ?

Lets define R(f(n),p) as the number of residue classes for f(n) mod p.

Conjecture : R(2^^n,p) < p - log(p) - slog(p)

where the log and slog are base 2.