11.2.6 - Application of Chinese Remainder Theorem
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Practice Questions
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What is the Chinese Remainder Theorem?
💡 Hint: Consider its relation to moduli.
Define coprime numbers.
💡 Hint: Think of prime numbers.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is guaranteed by the Chinese Remainder Theorem?
💡 Hint: Think about the uniqueness in systems of equations.
True or False: If two numbers are congruent mod m and m is prime, they are equal.
💡 Hint: Consider the possibilities outside of congruence.
1 more question available
Challenge Problems
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Prove that the CRT can be extended to more than two moduli.
💡 Hint: Think about the relationships of congruences.
If 17 and 19 are coprime moduli, find a number less than 323 that is congruent to 5 mod 17 and congruent to 12 mod 19.
💡 Hint: Calculate the respective products and their inverses.
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