Question Number 194689 by cortano12 last updated on 13/Jul/23
Answered by MM42 last updated on 13/Jul/23
$${f}_{{i}} :\mathrm{1},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{8},\mathrm{13},\mathrm{21},\mathrm{34},\mathrm{55},\mathrm{89},… \\ $$$$\Rightarrow\forall\:{n}=\mathrm{5}{k}\:\:;\:\mathrm{5}\mid{f}_{{n}} \:\:\:!!?? \\ $$$$\Rightarrow{if}\:\:{n}<\mathrm{10000}\:\rightarrow\:{ans}=\mathrm{4999}\:\checkmark \\ $$$${if}\:\:{f}_{{n}} <\mathrm{10000}\Rightarrow{n}\leqslant\mathrm{20}\Rightarrow{ans}=\mathrm{4} \\ $$