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I have a question regarding the number of real-valued super attractors. By a super attractor, I mean a complex number c such that 0 is mapped to 0 after n iterations, where the map is f(z) = z^2– c. The number of period-n super attractors is 2^(n-1) less the number of super attractors for each proper divisor of n.
Is it true that, if n is an odd prime, the number of real-valued super attractors is [2^(n-1) - 1]/n?