Implement the Chinese Remainder Theorem
Analyze the implement the chinese remainder theorem.
Examples
Input: "test_input_1"
Output: "output_1"
Input: "test_input_2"
Output: "output_2"
Hints
Start by understanding the problem statement of the Chinese Remainder Theorem (CRT) and its mathematical formulation. Recall that CRT provides a solution to a system of simultaneous congruences with pairwise coprime moduli.
Implement the extended Euclidean algorithm to compute the modular inverse, which is crucial for finding the solution to the congruences. Then, use this algorithm iteratively to combine the congruences into a single solution.
Generalize the solution to handle cases where the moduli are not pairwise coprime by first checking for consistency and then reducing the problem to the pairwise coprime case using the least common multiple (LCM) of the moduli.
Implement the Chinese Remainder Theorem
Analyze the implement the chinese remainder theorem.