The Chinese Remainder Theorem
Example. Find all integers x which leave a remainder of 1, 2, 3, and 4 when divided by 5, 7, 9, and 11 respectively. We are asked to solve the system of congruences: x 1 (mod 5) x 2 (mod 7) x 3 (mod 9) x 4 (mod 11): Notice that the moduli are pairwise relatively prime, as required by the theorem. We have M = 5 7 9 11 = 3465 and M 1 = M=5 = 693, 2 ................
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