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A219114
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Integers n such that n^2 is the difference of two Fibonacci numbers.
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6
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OFFSET
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1,3
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COMMENTS
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Numbers n such that n^2 is in A007298.
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LINKS
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EXAMPLE
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The only known square differences of Fibonacci numbers are:
0^2 = F(2)-F(1) = F(k)-F(k) for any k,
1^2 = F(1)-F(0) = F(2)-F(0) = F(3)-F(1) = F(3)-F(2) = F(4)-F(3),
2^2 = F(5)-F(1) = F(5)-F(2),
4^2 = F(8)-F(5),
9^2 = F(11)-F(6),
12^2 = F(12)-F(0) = F(13)-F(11) = F(14)-F(13),
15^2 = F(13)-F(6),
24^2 = F(15)-F(9).
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MATHEMATICA
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t = Union[Flatten[Table[Fibonacci[n] - Fibonacci[i], {n, 100}, {i, n}]]]; t2 = Select[t, IntegerQ[Sqrt[#]] &]; Sqrt[t2] (* T. D. Noe, Feb 12 2013 *)
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CROSSREFS
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Cf. A007298 (differences of Fibonacci numbers).
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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