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Question Number 42909 by naka3546 last updated on 04/Sep/18

How  many  pairs of  (a, b, c, d)  so  that           a! +  b!  +  c!  =  d!  which   a, b, c, d  ∈  positive  integers .

$${How}\:\:{many}\:\:{pairs}\:{of}\:\:\left({a},\:{b},\:{c},\:{d}\right)\:\:{so}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:{a}!\:+\:\:{b}!\:\:+\:\:{c}!\:\:=\:\:{d}! \\ $$$${which}\:\:\:{a},\:{b},\:{c},\:{d}\:\:\in\:\:{positive}\:\:{integers}\:. \\ $$

Answered by MJS last updated on 04/Sep/18

only 1: 2!+2!+2!=3!

$$\mathrm{only}\:\mathrm{1}:\:\mathrm{2}!+\mathrm{2}!+\mathrm{2}!=\mathrm{3}! \\ $$

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