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y 2 − x y − x 2 = 1 y^2 - xy - x^2 = 1 y2−xy−x2=1
Let ( x , y ) (x,y) (x,y)be the non-negative integer solutions to the hyperbolic graph above.
If x + y = n x+y = n x+y=nfor some perfect square n n n, what is the sum of all possible n ? n? n?
Hint:The only Fibonacci numbers that are perfect squares are 0, 1, and 144.
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