For C = 1 1 1 2 , it can be verified that C25 = 7,778,742,049 12,586,269,025
Chapter 10, Problem 4(choose chapter or problem)
For C = 1 1 1 2 , it can be verified that C25 = 7,778,742,049 12,586,269,025 12,586,269,025 20,365,011,074 It can also be verified that 12,586,269,025 is divisible by 101 and that when 7,778,742,049 and 20,365,011,074 are divided by 101, the remainder is 1. (a) Show that every point in S of the form (m/101, n/101) returns to its starting position after 25 iterations under Arnolds cat map. (b) Show that every point in S of the form (m/101, n/101) has period 1, 5, or 25. (c) Show that the point 1 101 , 0 has period greater than 5 by iterating it five times. (d) Show that (101) = 25.
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