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Omni-MATH / Let (F_(n)) be the sequence defined recursively by F₁=F₂=1 and F_(n+1)=F_(n)+F_(n−1) for n≥2. Find all pairs of positive integers (x,y) such that 5F_(x)−3F_(y)=1.

Problem

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problem

Let (Fn)(F_n) be the sequence defined recursively by F1=F2=1F_1=F_2=1 and Fn+1=Fn+Fn−1F_{n+1}=F_n+F_{n-1} for n≥2n\geq 2. Find all pairs of positive integers (x,y)(x,y) such that 5Fx−3Fy=1.5F_x-3F_y=1.
Plain-text mathematical notation (without MathML)
Let (F_(n)) be the sequence defined recursively by F₁=F₂=1 and F_(n+1)=F_(n)+F_(n−1) for n≥2. Find all pairs of positive integers (x,y) such that
5F_(x)−3F_(y)=1.
Original LaTeX notation
Let $(F_n)$ be the sequence defined recursively by $F_1=F_2=1$ and $F_{n+1}=F_n+F_{n-1}$ for $n\geq 2$. Find all pairs of positive integers $(x,y)$ such that
$$5F_x-3F_y=1.$$

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Source and history

task_id
154839bc-64fe-5a18-aab0-7611c590da50
task_key
test--154839bc-64fe-5a18-aab0-7611c590da50
task_revision_id
1
config / split
/ test

Official source

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