a) Show that the system of congruences.x: ? a2(modm1) and x ? a2 (mod m2), where a1, a2. m1, and m2 are integers with m1 >0 and m2 > 0, has a solution if and only if gcd(m1, m2) | a1 – a2.________________b) Show that if the system in part (a) has a solution, then it is unique modulo 1cm(m1, m2).

Solution Step 1:In part (a) we have to show that system of congruences and Where are integers with and ,has a solution if and only if