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Necessary condition to apply the Chinese remainder theorem is modulo of congruence should be:

Necessary condition to apply the Chinese remainder theorem is modulo of congruence should be: Correct Answer Relatively prime

Concept:

Chinese remainder theorem (CRT): Chinese remainder theorem is a method to solve a system of simultaneous congruence. One most important condition to apply CRT is the modulo of congruence should be relatively prime.

For example, consider simultaneous congruence relation

x ≡ a1 (mod m1),

x ≡ a2 (mod m2)

To apply CRT, m1 and m2 must be relatively prime.

Modulo of congruence: If two number a and b gives the same remainder when divided by m or difference 'a - b' is completely divisible by m, then m will be modulo of a and b.

Explanation:

As discussed above, we can say that the modulo of congruences should be relatively prime.

Related Questions

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