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

if f_n =f_(n−1) +f_(n−2) ; f_1 =f_2 =1 then prove that 5∣f_(5n)

iffn=fn−1+fn−2;f1=f2=1thenprovethat5∣f5n

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) ∀n≥3 ⇒ f_n =3f_(n−5) +5f_(n−4) ∀n≥6 5∣f_(n−5) ⇔ 5∣f_n ∀n≥6

f1=k1f2=k2fn=fn−1+fn−2∀n⩾3⇒fn=3fn−5+5fn−4∀n⩾65∣fn−5⇔5∣fn∀n⩾6

Commented by MM42 last updated on 13/Jul/23

that′s right

that′sright

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