Question Number 55701 by mathaddicted last updated on 02/Mar/19
$${Is}\:{true}\:{or}\:{not}\:{that}\:\mathrm{4181}\:{is}\:{the}\:{only}\:{one} \\ $$$${Fibonacci}'{s}\:{number}\:{with}\:{no}\:{prime}\:{factor} \\ $$$${which}\:{is}\:{also}\:{a}\:{Fibonacci}'{s}\:{number}? \\ $$
Commented by MJS last updated on 03/Mar/19
$$\mathrm{1346269}=\mathrm{557}×\mathrm{2417} \\ $$$$\mathrm{24157817}=\mathrm{73}×\mathrm{149}×\mathrm{2221} \\ $$$$... \\ $$
Answered by Kunal12588 last updated on 03/Mar/19
Commented by Kunal12588 last updated on 03/Mar/19
Commented by Kunal12588 last updated on 03/Mar/19
$$\mathrm{4181}\:{is}\:{the}\:\mathrm{20}{th}\:{term}\:{of}\:{the}\:{fibonacci}\:{series} \\ $$$${if}\:{started}\:{with}\:\mathrm{0}.\:{else}\:{its}\:\mathrm{19}{th}\:{term} \\ $$$$\mathrm{4181}=\mathrm{37}×\mathrm{113}\:{so}\:{its}\:{factors}\:{are}\:\mathrm{1},\mathrm{37},\mathrm{113},\mathrm{4181} \\ $$$${excluding}\:\mathrm{1}\:{and}\:\mathrm{4181}\:{itself} \\ $$$${factors}\:{of}\:\mathrm{4181}\:{are}\:\mathrm{37},\mathrm{113}\:{those}\:{were}\:{not} \\ $$$${a}\:{term}\:{of}\:{fibbonacci}\:{series}. \\ $$$${but}\:{there}\:{are}\:{other}\:{numbers}\:{also}\:{like} \\ $$$$\mathrm{233}−\:\mathrm{13}{th}\:{term}\:−\:{a}\:{prime}\:{number}\:{so}\:{it} \\ $$$$\:{does}\:{not}\:{have}\:{a}\:{factor}\:{which}\:{is}\:{a}\:{fibonacci}\:{number} \\ $$