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MATH / For n≥0, let F_(n) denote the nth Fibonacci number (that is, F₀=0,F₁=1, and F_(n)=F_(n−1)+F_(n−2) for all n≥2). What is the greatest possible value of the greatest common divisor o…

Problem

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problem

For n≥0n \ge 0, let FnF_n denote the nnth Fibonacci number (that is, F0=0,F1=1F_0 = 0, F_1 = 1, and Fn=Fn−1+Fn−2F_n = F_{n-1} + F_{n-2} for all n≥2n \ge 2). What is the greatest possible value of the greatest common divisor of two consecutive Fibonacci numbers?
Plain-text mathematical notation (without MathML)
For n≥0, let F_(n) denote the nth Fibonacci number (that is, F₀=0,F₁=1, and F_(n)=F_(n−1)+F_(n−2) for all n≥2). What is the greatest possible value of the greatest common divisor of two consecutive Fibonacci numbers?
Original LaTeX notation
For $n \ge 0$, let $F_n$ denote the $n$th Fibonacci number (that is, $F_0 = 0, F_1 = 1$, and $F_n = F_{n-1} + F_{n-2}$ for all $n \ge 2$). What is the greatest possible value of the greatest common divisor of two consecutive Fibonacci numbers?

level

Level 3

type

Number Theory

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Source and history

task_id
5f11a794-c54b-5ec8-89a8-40ed5ace545d
task_key
number~5ftheory--test--5f11a794-c54b-5ec8-89a8-40ed5ace545d
task_revision_id
1
config / split
number_theory / test

Official source

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