Is there a positive integer
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
such that the equation
![{1\over a}+{1\over b}+{1\over c}+{1\over abc}={m\over a+b+c}](/media/m/c/5/f/c5f3f750e6900e779d14d7d8617cbda8.png)
has infinitely many solutions in positive integers
![a,b,c](/media/m/3/6/4/36454fdb50fc50f021324b33a6b513e3.png)
?
%V0
Is there a positive integer $m$ such that the equation $${1\over a}+{1\over b}+{1\over c}+{1\over abc}={m\over a+b+c}$$ has infinitely many solutions in positive integers $a,b,c$?