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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