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CTK Exchange
amphibius jones
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Mar-29-08, 00:05 AM (EST) |
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"Integer Points on a Circle"
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The page for this interesting problem
https://www.cut-the-knot.org/SimpleGames/IntIter.shtml
seems to contain glaring errors. The statement that the only way to get a sequence of all equal numbers is for the previous sequence to be all even or all odd is definitely false. Simply consider 1212 which yields 1111. The same oversight appears later in the page when it is stated that only nonconstant sequences converge when N is a power of 2. Again, 121212 is a sequence of 6 which clearly converges to zeros (of course this counterexample extends to any even N). In fact, one checks that up to translation, scaling, rotation and reflection, there are exactly three nonzero sequences of length six which converge to zeros. Is there some restriction on the sequences that isn't mentioned (or that I missed)? |
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