# Unique Hyperbola

$y^2 - xy - x^2 = 1$

Let $$(x,y)$$ be the non-negative integer solutions to the hyperbolic graph above.

If $$x+y = n$$ for some perfect square $$n$$, what is the sum of all possible $$n?$$

Hint: The only Fibonacci numbers that are perfect squares are 0, 1, and 144.

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