Menu Close

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-




Question Number 60915 by naka3546 last updated on 27/May/19
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_(2019)  .
$${Let}\:\:{Fibonacci}\:\:{sequence}\:\:\left({F}_{{n}} \right)\:_{{n}\geqslant\mathrm{0}} \\ $$$${where}\:\:{F}_{\mathrm{0}} \:=\:\mathrm{0},\:{F}_{\mathrm{1}} \:=\:\mathrm{1},\:\:{and}\:\:{F}_{{n}+\mathrm{2}} \:\:=\:\:{F}_{{n}+\mathrm{1}} \:+\:{F}_{{n}} \:\:\:\:,\:\:\forall\:{n}\:\:\geqslant\:\:\mathrm{0}\:. \\ $$$${Find}\:\:{the}\:\:{least}\:\:{of}\:\:{natural}\:\:{numbers}\:\:{n}\:\:{so}\:\:{that} \\ $$$${F}_{{n}} \:\:\:{and}\:\:\:{F}_{{n}+\mathrm{1}} \:−\:\mathrm{1}\:\:\:{can}\:\:{be}\:\:{divided}\:\:{by}\:\:\:{F}_{\mathrm{2019}} \:. \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *