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Omni-MATH / The Fibonacci sequence F₁,F₂,F₃,… is defined by F₁=F₂=1 and F_(n+2)=F_(n+1)+F_(n). Find the least positive integer t such that for all n>0,F_(n)=F_(n+t).

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The Fibonacci sequence F1,F2,F3,…F_{1}, F_{2}, F_{3}, \ldots is defined by F1=F2=1F_{1}=F_{2}=1 and Fn+2=Fn+1+FnF_{n+2}=F_{n+1}+F_{n}. Find the least positive integer tt such that for all n>0,Fn=Fn+tn>0, F_{n}=F_{n+t}.
Plain-text mathematical notation (without MathML)
The Fibonacci sequence F₁,F₂,F₃,… is defined by F₁=F₂=1 and F_(n+2)=F_(n+1)+F_(n). Find the least positive integer t such that for all n>0,F_(n)=F_(n+t).
Original LaTeX notation
The Fibonacci sequence $F_{1}, F_{2}, F_{3}, \ldots$ is defined by $F_{1}=F_{2}=1$ and $F_{n+2}=F_{n+1}+F_{n}$. Find the least positive integer $t$ such that for all $n>0, F_{n}=F_{n+t}$.

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Source and history

task_id
8fb568b2-c755-546c-86da-d2f1bf9ad3ed
task_key
test--8fb568b2-c755-546c-86da-d2f1bf9ad3ed
task_revision_id
1
config / split
/ test

Official source

initial import