10.2 - Solving Linear Congruences using Extended Euclid's Algorithm
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Practice Questions
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What are the conditions under which a linear congruence has a unique solution?
💡 Hint: What do we mean by the coefficients being coprime?
Solve the linear congruence 4x ≡ 2 (mod 6).
💡 Hint: Check if a and n share common factors.
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Interactive Quizzes
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What does it mean for two numbers to be coprime?
💡 Hint: Think about the GCD definition.
True or False: The Chinese Remainder Theorem can find solutions for any moduli.
💡 Hint: Consider the requirements for CRT to work.
1 more question available
Challenge Problems
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Solve the system of congruences: x ≡ 1 (mod 2), x ≡ 2 (mod 3), x ≡ 3 (mod 4). Show your work and verify all solutions.
💡 Hint: Break down each congruence systematically.
Apply the Extended Euclidean Algorithm to determine the inverse of 14 modulo 33, then solve 14x ≡ 11 (mod 33).
💡 Hint: Look for steps in the algorithm outlining the GCD.
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