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Topic: A Characterization of Fibonacci Numbers (Read 453 times) |
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Aryabhatta
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A Characterization of Fibonacci Numbers
« on: May 13th, 2008, 4:51pm » |
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Show that a positive integer f is a Fibonacci number if and only if one of {5f2+4, 5f2-4} is a perfect square.
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towr
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Re: A Characterization of Fibonacci Numbers
« Reply #1 on: May 14th, 2008, 9:44am » |
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Possibly a start, possibly not.
g1=1
g2=3
gn+2=gn+1+gn
odd n: gn2 = 5fn2 - 4
even n: gn2 = 5fn2 + 4
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| « Last Edit: May 14th, 2008, 9:44am by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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Barukh
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Re: A Characterization of Fibonacci Numbers
« Reply #2 on: May 14th, 2008, 10:23am » |
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Lucas numbers and Pell equations?
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Eigenray
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Re: A Characterization of Fibonacci Numbers
« Reply #3 on: May 14th, 2008, 1:23pm » |
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Or, fundamental unit of a real quadratic number field.
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Aryabhatta
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Re: A Characterization of Fibonacci Numbers
« Reply #4 on: May 14th, 2008, 3:32pm » |
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Yup. Well done people!
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