**For the following equation:-**
$$a\_1+a\_2+a\_3.....+a\_n=a\_1a\_2a\_3.....a\_n = n$$  
For $a\_1,a\_2...a\_n \in \mathbb Z$, find the general form of the ***integer*** n.  

Note that we need $n$ summands/factors

**Note:-** Regarding the explanation of the term "general form":  
 For instance, even numbers are of the general form $2m.$ and rational numbers are of the general form $p/q,etc $. I mean it in that way.  

PS: My guess is that we have to use some general formula for multivariable diophantine equation but I don't even know what to do if it is a multivariable diophantine equation.