A third argument returns the smallest solution greater than or equal to it.
$ wo 'ChineseRemainder[{1, 2}, {3, 5}, 10]'
22
Without congruences there is nothing to solve, so the call is left unevaluated.
$ wo 'ChineseRemainder[{}, {}]'
ChineseRemainder[{}, {}]
Lists of differing length are reported as an argument error.
$ wo 'ChineseRemainder[{1, 2}, {3}]'
ChineseRemainder::pilist: The arguments to ChineseRemainder must be two lists of integers of identical length, with the second list containing only positive integers.
ChineseRemainder[{1, 2}, {3}]