Fibonacci squares?

Number Theory Level pending

The Fibonacci numbers are given by:

\(0,1,1,2,3,5,8,13,21....\)

And in general they satisfy the following recursion relation:

  • \(F(0) = 0\)
  • \(F(1) = 1\)
  • \(F(n) = F(n-2) + F(n-1)\) for \(n > 1\)

For how many Fibonacci numbers does \(F(n) = n^2\) ?

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