# Understanding Modular Arithmetic

Suppose that we are given: $$1124 \cdot 5097 \equiv x \mod 5693$$

Then $x = 1870$ since $(1124 \cdot 5097) -x = 5693k$ if $k=1006$.

Is this correct? I'm not exactly sure how to think about these types of problems. It seems that I could simply do $$(1124 \cdot 5097)\mod 5693 = 1870$$ If someone could please explain how to approach these types of problems, that would be greatly appreciated.

In this specific case, you can just multiply the numbers out, then find the remainder. If, on the other hand, you had $a*x\equiv b\mod c$, you would need to find $a^{-1}\mod c$ and multiply both sides by it.