little_dragon wrote:how do u no?
Let the original numbers be "a" and "b", the divisor be "d", and the equal remainder be "r". Then, by definition of division, etc, we get:
a = md + r
b = nd + r
(The "m" and "n" will be the answers across the top of the long division, the part that "d" went "evenly" into. This is like "thirteen divided by four has a remainder of one" can also be written as "13 = 3*4 + 1".)
The difference then is:
(md + r) - (nd + r) = md - nd = (m - n)d
So the divisor must divide the differences.
Hope that made sense!