11.2.3 - Uniqueness Proof Part for the Chinese Remainder Theorem
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Practice Questions
Test your understanding with targeted questions
Explain Euclid's Lemma in your own words.
💡 Hint: Think of how primes work with products.
What does it mean for numbers to be 'pairwise relatively prime'?
💡 Hint: Look at pairs of numbers and their factors.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does Euclid's Lemma state?
💡 Hint: Think of how primes operate in multiplication.
True or False: If a system of linear congruences has more than one solution, they must be congruent modulo M.
💡 Hint: Consider the implications of congruence properties.
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Challenge Problems
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Given three integers 4, 6, and 10, demonstrate using CRT that a linear combination of these can yield a unique solution within a defined modulus that is their product.
💡 Hint: Break down each modulus and product relation carefully.
Suppose there are solutions x1 and x2 for a given set of linear equations. Show that if these solutions yield differing results, it contradicts the uniqueness principle established in CRT.
💡 Hint: Bring in the notion of divisibility and modulo relations.
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