if-f-n-f-n-1-f-n-2-f-1-f-2-1-then-prove-that-5-f-5n-

Question Number 194693 by MM42 last updated on 13/Jul/23

i f f_{n} = f_{n - 1} + f_{n - 2}; f_{1} = f_{2} = 1

t h e n p r o v e t h a t 5 ∣ f_{5 n}

Answered by Frix last updated on 13/Jul/23

f_{1} = k_{1}

f_{2} = k_{2}

f_{n} = f_{n - 1} + f_{n - 2} \forall n ⩾ 3

\Rightarrow

f_{n} = 3 f_{n - 5} + 5 f_{n - 4} \forall n ⩾ 6

5 ∣ f_{n - 5} \Leftrightarrow 5 ∣ f_{n} \forall n ⩾ 6

Commented by MM42 last updated on 13/Jul/23

{t h a t}^{'} s r i g h t

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