Find all integral solutions to $a+b+c=abc$. Find all integral solutions of the equation $a+b+c=abc$.  
Is $\{a,b,c\}=\{1,2,3\}$ the only solution? I've tried by taking $a,b,c=1,2,3$.

a+b+c=abc then first of all (a+b+c)>=3*(abc)^1/2 so (abc)^2>=9abc so abc>=9 which shows that a+b+c>=9 which is strictly impossible to satisfy for integer.
Other way is to think that first of all 0 being obvious solution and for other solution let a+c=0 then
b=-aab
Which again gives 0 as the only solution
a+b+c=abc
(1/ab)+(1/bc)+(1/ca)=1 which is only possible for ab=2,bc=3,ca=6 which again yields no solutions.I mean different solutions i.e another equal to b & so on.
