For some integers a,b, a=b (mod x). Find x in terms of a and b.

It appears the answer is a-b, but I'm not sure how to prove it without modular arithmetic, which I don't really understand.

Is there a simple way to prove and explain this without mods?

Guest Dec 7, 2018

#1**+1 **

What I'm seeing is that if you take the prime factors of (a-b) as a set

And take all length permutations of that set and then take the product of the elements in that permutation

All those values will be values of x such that a = b mod x

I don't know of any way to show this without using any modular arithmetic at all.

Rom Dec 7, 2018