In computer science, more specifically, the theory of finite automata, the Chinese Remainder Theorem proves useful when thinking about finite automata or regular expressions over a 1-letter alphabet. The prerequisites (finite automata, regular expressions, NP-completeness) for understanding these applications are usually taught in "introduction to theoretical computer science" university courses.

For example, the universality problem for unary regular expressions is coNP-complete. The polynomial-time reduction uses chinese remaindering to encode a boolean formula into a regular expression. L. J. Stockmeyer, A. R. Meyer: Word problems requiring exponential time (Preliminary Report), Proceedings of the th annual ACM symposium on Theory of computing (STOC '73), pp. 1-9.

Also, the worst-case size blowup when moving from nondeterministic to deterministic finite automata is related to Landau's function, and the proof uses the Chinese Remainder Theorem. Marek Chrobak: Finite Automata and Unary Languages. Theoretical Computer Science 47(3): 149-158 (1986)