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.