# Theory of numbers – Verification of divisibility in different modules.

So I'm working on modular arithmetic and I found the following problem:

Assume that $$a cdot b mod m = c$$ and that I know $$c mod n = d$$. Can I still check the divisibility of $$c$$ using $$d$$? A quick check tells me to check if $$d mod n = 0$$ It does not work, but it is impossible to perform this check or there is a general way to find out if $$c | a$$? Maybe yes $$m$$ Y $$n$$ they are cousins?

Thank you!