<s>[INST] How to get the value of $a + b + c$? $(0 \leq a  < b < c) \in Z$,
$a + b + c + ab + ac + bc + abc = 1622$
$a + b + c = ?$
I've assumed that $a = 0$, by that we can get rid of this part $ab + ac + abc$
Now $bc + b + c = 1622$.
But I found that was useless and got stuck. 
 [/INST] Note that $$1+a+b+c+ab+bc+ca+abc=(1+a)(1+b)(1+c)$$
$$(1+a)(1+b)(1+c)=1623=1\cdot3\cdot541$$
$$\implies a=0,\ b=2,\ c=540.$$
Note that $0\leq a<b<c$. Those three numbers, 1, 3 and 541 are the only possible factorisation that could satisfy this criteria
</s>