8.17 A common formulation of the Chinese remainder theorem (CRT) is as follows: Let m1,..., mk be integers that are pairwise relatively prime for 1 i, j k, and i j. Define M to be the product of all the mi"s. Let a1,..., ak be integers. Then the set of congruences: x = a1(mod m1) x = a2(mod m2) . . . x = ak(mod mk) has a unique solution modulo M. Show that the theorem stated in this form is true. | |
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