10 - Linear Congruence Equations and Chinese Remainder Theorem
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Practice Questions
Test your understanding with targeted questions
What does the notation a ≡ b (mod N) mean?
💡 Hint: Think about the definition of congruence.
If x ≡ 3 (mod 5), what could be a value of x?
💡 Hint: Find such numbers by adding multiples of 5.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the condition for using the extended Euclidean algorithm?
💡 Hint: What condition does the existence of an inverse require?
True or False: The Chinese Remainder Theorem guarantees a unique solution for any set of congruences.
💡 Hint: Think about the conditions of the theorems discussed.
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Challenge Problems
Push your limits with advanced challenges
Using the Chinese Remainder Theorem, solve for x in the system: x ≡ 1 (mod 4), x ≡ 3 (mod 5), x ≡ 2 (mod 7).
💡 Hint: Determine the product of moduli and work through the steps of CRT.
Show that x ≡ 5 (mod 15) has infinitely many solutions, and list at least three.
💡 Hint: Use the general formula for solutions in linear congruences.
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