Arithmetic string equal to the geometric string, count x

[ghostfirefox]

Let x1, ..., x25 be such positive integers that x1⋅x2⋅ ... ⋅x25 = x1 + x2 + ... + x25. What is the maximum possible value of the largest of numbers x1, x2, ..., x25?

[HallsofIvy]

What exactly do you mean by "x1- x2...- x25? Am I correct that each term after the first is subtracted and this is NOT an alternating sum? If so then you have x1- (x2+ ...+ x25)= x1+ (x2+ ...+ x25) so that -(x2+ ...+ x25)= X2+ ...+ X25 and then 2(x2+ ...+ x25)= 0 so x2+ ...+ x25= 0. There is NO "largest possible value" since, if x2+ ...+ x25= 0, x1 can be any number at all.