8.17 A common formulation of the Chinese remainder theorem (CRT) is as follows: Let m1,c, 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,c, ak be integers. Then the set of congruences:
has a unique solution modulo M. Show that the theorem stated in this form is true.