Let's say we have a\equiv x\mod b and a\equiv y\mod c. Is there any way to find the relationship between x and y for nontrivial (a>b and/or a>c) moduli?
How about a specific example, such as
a\equiv x\mod b vs a\equiv y\mod 2b,
or
a\equiv x\mod b vs a\equiv y\mod 2b-1.
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