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GAIC Math 2024 Problem 60

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Assuming sequence Fn{F_n} satisfying: F1=F2=1,Fn+1=Fn+Fn−1(n≥2)F_1=F_2=1, F_{n+1}=F_n+F_{n-1} (n\geq 2). Then the number of sets of positive integers (x,y)(x,y) that satisfy 5Fx−3Fy=15F_x-3F_y=1 is

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