We will say that two positive integers, n_i and n_j are relatively prime if the greatest common divisor of n_i and n_j is 1. Suppose that we are given a system of equations: x = a_1 mod n_1 x = a_2 mod n_2 x = a_m mod n_m where each n_i and n_j are relatively prime for i notequalto j. For N = Pi_i = 1^m n_i, give an efficient algorithm to compute a solution to this system of equations x that is between 0 and N - 1. Show that x {0, 1, ..., N - 1} is uniquely determined by a_1 {0, 1, ..., n_1 - 1}, a_2 {0, 1, ..., n_2 - 1}, ..., a_m {0, 1, ..., n_m - 1} and vice versa. That is that for each such system of equations there is a unique solution, and for each such x (and fixed n_1, n_2, ..., nm) there is a unique system of equations for which z is a solution. We will say that two positive integers, n_i and n_j are relatively prime if the greatest common divisor of n_i and n_j is 1. Suppose that we are given a system of equations: x = a_1 mod n_1 x = a_2 mod n_2 x = a_m mod n_m where each n_i and n_j are relatively prime for i notequalto j. For N = Pi_i = 1^m n_i, give an efficient algorithm to compute a solution to this system of equations x that is between 0 and N - 1. Show that x {0, 1, ..., N - 1} is uniquely determined by a_1 {0, 1, ..., n_1 - 1}, a_2 {0, 1, ..., n_2 - 1}, ..., a_m {0, 1, ..., n_m - 1} and vice versa. That is that for each such system of equations there is a unique solution, and for each such x (and fixed n_1, n_2, ..., nm) there is a unique system of equations for which z is a solution