chinese remainder theorem tutorialspoint

How do you find the solution of the Chinese remainder theorem?
Process to solve systems of congruences with the Chinese remainder theorem:
1Begin with the congruence with the largest modulus, x ≡ a k ( m o d n k ) .
2) Substitute the expression for x x x into the congruence with the next largest modulus, x ≡ a k ( m o d n k ) ⟹ n k j k + a k ≡ a k − 1 ( m o d n k − 1 ) .
The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers.

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