5. (20 pts) A conjecture is a statement which is probably true but has not been proved or disproved. In this problem, we will "discover" a conjecture. a) (5 pts) Start with any positive integer. If it is even, divide by 2. If it is odd, multiply by 3 and add 1. So, we have a new integer, use the same rule to generate the next integer. Repeat and record the sequence of integers until it is natural to stop. b) (5 pts) Repeat part (a) with another initial positive integer. c) (10 pts) Write down a conjecture based on your observation in parts (a) and (b). Feel free to do more experimentation.

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