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The question

 Mar 20, 2023
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To find the smallest positive integer m such that c^m(9) = 1, we need to repeatedly apply the function c to the previous result until we reach 1.

Starting with c(9) = 28, we can continue to apply c to the result until we get back to 1:

c(28) = 14 c(14) = 7 c(7) = 22 c(22) = 11 c(11) = 17 c(17) = 52 c(52) = 26 c(26) = 13 c(13) = 40 c(40) = 10 c(10) = 5 c(5) = 16 c(16) = 8 c(8) = 4 c(4) = 2 c(2) = 1

 

We can see that the sequence eventually reaches the number 1, but it takes 17 steps. Therefore, we have c^17(9) = 1. This means that the smallest positive integer m such that c^m(9) = 1 is m = 17.

 Mar 20, 2023

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