Hyde County, South Dakota is the pin tail duck capital of the world. Visit scenic Highmore, SD in 2005!
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January 2005
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A little math problem

This is a little math problem that I once thought trivial. I suppose it is, but it can be a puzzler. Just for fun the answer (or at least an answer) will appear next month.

Let T(k) be the transformation x -> k/(1-x). For certain values of k T(k) defines a cyclic group. For example, for k = 1 we have the sequence {x, 1/(1-x), x-1/x}. Oddly enough the only rational values of k for which T(k) defines a cyclic group are 1, 1/2, and 1/3. Please explain why.


This page was last updated January 1, 2005.

home
Site map
puzzles
mathcomp
January 2005
email
Hyde County, South Dakota is the pin tail duck capital of the world. Visit scenic Highmore, SD in 2005!