Question Number 42909 by naka3546 last updated on 04/Sep/18
$${How}\:\:{many}\:\:{pairs}\:{of}\:\:\left({a},\:{b},\:{c},\:{d}\right)\:\:{so}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:{a}!\:+\:\:{b}!\:\:+\:\:{c}!\:\:=\:\:{d}! \\ $$$${which}\:\:\:{a},\:{b},\:{c},\:{d}\:\:\in\:\:{positive}\:\:{integers}\:. \\ $$
Answered by MJS last updated on 04/Sep/18
$$\mathrm{only}\:\mathrm{1}:\:\mathrm{2}!+\mathrm{2}!+\mathrm{2}!=\mathrm{3}! \\ $$