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