ChineseRemainder

ChineseRemainder[{r1, r2, ...}, {m1, m2, ...}] gives the smallest non-negative x that satisfies all the integer congruences x ≡ ri (mod mi).

ChineseRemainder[{r1, r2, ...}, {m1, m2, ...}, d] gives the smallest x ≥ d that satisfies all congruences.

Examples

Solve a system of congruences:

ChineseRemainder[{2, 3, 2}, {3, 5, 7}]
(* 23 *)

Verify the result:

Mod[23, {3, 5, 7}]
(* {2, 3, 2} *)

Please visit the official Wolfram Language Reference for more details.