Because the original equation has six natural number solutions, the original equation can be solved into three equations, each factor =0 (and they are different, that is, c 1, c2 and c3 are different; The relationship between the three equations is or). That is to say, each factor can be decomposed into the form of (x-a)(x-b) within the range of rational numbers (where A and B are the solutions of the original equation and are different natural numbers, satisfying a+b=6, ab=c 1, c2, c3). Therefore, according to natural numbers A and B, if a+b=6, we can get A, b=0 and 6 or 1 and 5 or 2 and 4. So c 1, c2 and c3 are both 0 or 5 or 8, so the maximum difference is 8-0=8.