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%I #14 Jun 12 2015 08:23:43
%S 0,1,2,4,9,12,15,24
%N Integers n such that n^2 is the difference of two Fibonacci numbers.
%C Numbers n such that n^2 is in A007298.
%C No other terms below 10^10000. - _Manfred Scheucher_, Jun 12 2015
%H MathOverflow, <a href="http://mathoverflow.net/questions/84797">Can the difference of two distinct Fibonacci numbers be a square infinitely often?</a>
%H Manfred Scheucher, <a href="/A219114/a219114.sage.txt">Sage Script</a>
%e The only known square differences of Fibonacci numbers are:
%e 0^2 = F(2)-F(1) = F(k)-F(k) for any k,
%e 1^2 = F(1)-F(0) = F(2)-F(0) = F(3)-F(1) = F(3)-F(2) = F(4)-F(3),
%e 2^2 = F(5)-F(1) = F(5)-F(2),
%e 4^2 = F(8)-F(5),
%e 9^2 = F(11)-F(6),
%e 12^2 = F(12)-F(0) = F(13)-F(11) = F(14)-F(13),
%e 15^2 = F(13)-F(6),
%e 24^2 = F(15)-F(9).
%t 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 *)
%Y Cf. A000045 (Fibonacci numbers).
%Y Cf. A007298 (differences of Fibonacci numbers).
%K nonn,hard,more
%O 1,3
%A _Max Alekseyev_, Nov 12 2012
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