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Exercise 1.5. This problem is about the periodic points of F(x)=x22 as in Example 1.6....

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Exercise 1.5. This problem is about the periodic points of F(x)=x22 as in Example 1.6. As mentioned there, the number of solutions of Fn(x)=x is P(n)=2n. a. Find the number of periodic points of F(x)=x22 of minimal periods q= 1,2,12. b. Suppose q is a prime number. What is Q(q) ? c. Prove that Q(q)>0 for all q1, that is, F has at least one periodic point of every possible minimal period q. Hint: Clearly Q(d)2d for all d. Use (6) together with the fact that any proper divisor d0 for all q1, that is, F has at least one periodic point of every possible minimal period q. Hint: Clearly Q(d)2d for all d. Use (6) together with the fact that any proper divisor d<><> <><>

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