Consider the following function from the positive integers to itself. For a positive integer x, let f(x) = x/2 if x is even; otherwise, let f(x) = 3x+1. The 3x+1 problem conjectures that for each integer x some iteration f applied to x yields 1. Recently, Charles C. Cadogan has claimed the first positive solution to this problem. This elementarily stated problem is due to L. Collatz in 1937, and is therefore also known as the Collatz Conjecture. It has enthused both serious mathematicians as well as amateurs. Byran Thwaites of the UK has offered a £1000 prize for the solution to this problem also known as Hasse's algorithm, Kakutani's problem, Syracuse algorithm, Syracuse problem, Thwaites conjecture, and Ulam's problem.

There appears to be a whole in the proof.


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