Let m1, m2, . . . , mn be pairwise relatively prime integers greater than or equal to 2. Show that if a ≡ b (mod mi) for i = 1, 2, . . . , n, then a ≡ b (mod m), where m = m1m2 · · ·mn. (This result will be used in Exercise 30 to prove the Chinese remainder theorem. Consequently, do not use the Chinese remainder theorem to prove it.)