Find all m so that 1066 $\equiv$ 1776 (mod m).

Question

I know to find the positive integers, you have 1776-1006 = 710 and then find all the divisors of 710 which is 1,2,5,10,71,142,355 and 710. But how do you find the negative integers for this question?

Answer 1

If $1066 \equiv 1776 $ (mod m), then $710 \equiv 0$ (mod m).

You then found all the positive factors of $710$ because they satisfy $710 \equiv 0$ (mod m).

It turns out all negative factors satisfy this equivalence too!

For example, $710$ is still an integer multiple of $-142$.