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HMMT 2003 U6

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Define the Fibonacci numbers by F0=0,F1=1,Fn=Fn−1+Fn−2F_{0}=0, F_{1}=1, F_{n}=F_{n-1}+F_{n-2} for n≥2n \geq 2. For how many n,0≤n≤100n, 0 \leq n \leq 100, is FnF_{n} a multiple of 13 ?

Dataset text NuminaMath olympiads. Quoted with source.

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