10.4 - Statement of the Chinese Remainder Theorem
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Practice Questions
Test your understanding with targeted questions
What is the general solution form of a linear congruence?
💡 Hint: Consider how many solutions exist once you find one.
Define pairwise coprime.
💡 Hint: Think about how many numbers share divisors.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the form of solutions for linear congruences?
💡 Hint: Think about the structure of solutions.
True or False: The Chinese Remainder Theorem guarantees a unique solution if the moduli share a common factor.
💡 Hint: Recall the conditions for application of CRT.
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Challenge Problems
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Demonstrate the application of the Chinese Remainder Theorem by forming and solving a system of congruences for a fictional age scenario.
💡 Hint: Set up equations reflecting given ages and moduli.
Given the congruences x ≡ 1 (mod 6), x ≡ 5 (mod 9), and x ≡ 3 (mod 10), apply the CRT to find the smallest positive solution.
💡 Hint: Use the method of constructing equations based on defined remainders.
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