(In reply to preliminary computer results (spoiler)
Is there any reason to assume that each of a,b,c is a positive number?
995<x < 31427 does not imply this.
IMHO the above statement leads to the conclusion that the range of numbers needed to find ALL solutions by an exhaustive search is infinite thus precluding trying.
A triplet like a=10^25, b=55-10^25, c=1 is within a+b+c definition. So is a=25000, b=-1000, c=1000.
My suggestion: Stay with your program solution, change the puzzle wording: i.e. positive instead of nonzero.
Edited on June 10, 2013, 6:35 am