I've tried searching but I haven't been able to find an answer. There are similar questions about reversing modulo operation here on stackexchange, but I haven't found a question which is applicable to my problem.
All answers I've found on reversing modulo says that you cannot uniquely determine the original answer. (At least if I understand them right.)
But let's say we know that:
$x \!\mod 10 = 13\ $ and $\ x \!\mod 13 = 2$.
Can we with this method uniquely determine $x$ if we have $n$ amount of these equations? I'm guessing that if $n \rightarrow \infty$ we can do it, but would this be the only case?
I hope I'm making sense, thanks!