Show that the system of congruences {x = a1 mod m1, x = a2 mod m2)...

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Show that the system of congruences {x = a1 mod m1, x = a2 mod m2) has a solution if and only if (m2-m1)|(a2-a1). Show that when there is a solution, it is unique modulo [m1, m2]. (Hint: Write the first congruence as x = a1 + km1, where k is an integer, and then insert this expression for x into the second congruence. Show that the system of congruences {x = a1 mod m1, x = a2 mod m2) has a solution if and only if (m2-m1)|(a2-a1). Show that when there is a solution, it is unique modulo [m1, m2]. (Hint: Write the first congruence as x = a1 + km1, where k is an integer, and then insert this expression for x into the second congruence.