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.