LinearRecursion

Problem - 2261
Let $F(1)=1, F(2)=1, F(n+2)= F(n+1)+F(n)$ be the Fibonacci sequence. Prove if $i | j$, then $F(i) | F(j)$. Or described in another way, every $k^{th}$ element is a multiple of $F(k)$.

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