Let a, b be two integers and let p, q be two distinct primes. Suppose that the two congruences… 1 answer below »

Let a, b be two integers and let p, q be two distinct primes.

Suppose that the two congruences x = a (mod p) and x =

b (mod q) have a simultaneous solution x0. Prove that this solution is unique modulo pq. That is prove that if x1 is another

simultaneous solution, then x0 = x1 (mod pq).

 
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