Let n1, n2, n3 be three numbers that are pairwise relatively prime so that (n1, n2) = (n2, n3) = (n1, n3). Let a1, a2, and a3 be any integers. We showed in class that the system x ≡ a1 (mod n1) x ≡ a2 (mod n2) x ≡ a3 (mod n3) has a unique solution, say b, modulo n1n2n3. Give a formula for b in terms of a1, a2, a3, n1, n2, and n3. You will need to make use of multiplicative inverses.

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