Choose the false statement:
Choose the false statement: Correct Answer A number is called modulus if the sum or If difference of two numbers is integrally divisible by that number.
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:
- To apply Chinese remainder theorem, moduli of linear congruence should be co-prime. Hence this is the correct statement.
- A number is called modulus if the sum or if a difference of two numbers is integrally divisible by that number. This is the wrong statement, as the necessary condition is a difference of two number should be divisible by that number.
Therefore, from the above discussion, we can conclude that Option 2 is the correct answer of above question.
