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Suppose that n and K are positive integers. A seven-term sequence is built using the following rules:
• The first term of the sequence is n.
• If a term of the sequence is even, divide by 2 to get the next term.
• If a term of the sequence is odd, multiply by K and add 1 to get the next term.
For example, if n = 9 and K = 3, the sequence is 9, 28, 14, 7, 22, 11, 34.
K is chosen such that there exists an n so that the first and seventh terms of the sequence are both n.
(a) Show that K must be odd.
(b) Find, with proof, all possible values of K.

 Mar 27, 2021
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Do you have any specif numbers for K or do you just want them to be odd?

 

-wolfie ^-^

 Mar 27, 2021

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