I was thinking you could maybe get a little further because you know x_n was an integer and you could define:

since x_n was an integer, x_n = y / (n - 1) where y is an integer (1 + sum...). I haven't tried it yet, but I wonder if you sub that in to the x_{n+1}, does it get you any further (does that (n-1) cancel anything out). The next step has got to be that you take advantage of the fact that you know the previous number was an integer ........

ms