(a) Assume that n1, n2 and n3 are integers with gcd(n1, n2) = gcd(n2, n3) = gcd(n1, n3) = 1. Let a1,az and az be integers and let N1 = nzn3, N2 = n¡n3 and N3 = nịn2. Consider the integer 1= a,N1) + ażNw2) + azN(ma). Prove that r = ɑ1 mod n1, 1 = az mod n2 and z = a3 mod n3 (b) Use part (a) to find a solution to the system of congruences I = 3 mod 8, I = 2 mod 3, r=1 mod 5

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