Let Fibonacci sequence (F_n ) _(n≥0) where F_0 = 0, F_1 = 1, and F_(n+2) = F_(n+1) + F_n , ∀ n ≥ 0 . Find the least of natural numbers n so that F_n and F_(n+1) − 1 can be divided by F


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Question Number 60915 by naka3546 last updated on 27/May/19

$L e t F i b o n a c c i s e q u e n c e (F_{n})_{n ⩾ 0}$ $w h e r e F_{0} = 0, F_{1} = 1, a n d F_{n + 2} = F_{n + 1} + F_{n}, \forall n ⩾ 0 .$ $F i n d t h e l e a s t o f n a t u r a l n u m b e r s n s o t h a t$ $F_{n} a n d F_{n + 1} - 1 c a n b e d i v i d e d b y F_{2019} .$
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