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A117045
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Integers k (not perfect squares) such that the continued fraction expansion of the square root of k has period at most 2.
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0
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2, 3, 5, 6, 8, 10, 11, 15, 17, 18, 20, 24, 26, 27, 30, 35, 37, 38, 39, 40, 42, 48, 50, 51, 56, 63, 65, 66, 68, 72, 80, 82, 83, 84, 87, 90
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OFFSET
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1,1
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COMMENTS
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In a recent paper, Justin Thomas, Julian Rosen, and I show that this is equivalent to the following criterion: let d be the integer part of the square root. Then sqrt(k) has period at most 2 if and only if 2d/(k - d^2) is an integer.
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REFERENCES
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Justin Thomas, Krishnan Shankar, Julian Rosen, "Continued Fractions, Square Roots and the orbit of 1/0 on the boundary of the hyperbolic plane", preprint.
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LINKS
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EXAMPLE
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The first term is 2 because sqrt(2) is irrational and for k=2, d=1, 2d/(k - d^2) = 1 is an integer.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Krishnan Shankar (shankar(AT)math.ou.edu), Apr 17 2006
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STATUS
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approved
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