I was trying to do this:
For any integer $n\ge2$, find $n$ numbers $a_1,\ a_2,\ a_3,\dots,a_n$ such that $$a_1+a_2+a_3+\dots+a_n=a_1a_2a_3\dots a_n$$
For $n=2$, we have $a_1=a_2=2$. (As $2+2=2\times2)$
For $n=3$, we have $a_1=1,\ a_2=2,\ a_3=3.$ ($1+2+3=1\times2\times3$)
Do there exist any such numbers for higher values of $n$ (i.e $n\ge4$). If there are give such examples. If there don't exist such numbers for $n\ge4$, there must be a proof from elementary number theory for this. What is that proof?