Practice Solving Linear Congruences Using Extended Euclid's Algorithm (10.2) - Linear Congruence Equations and Chinese Remainder Theorem

Practice: Solving Linear Congruences using Extended Euclid's Algorithm

Lesson 10.2Linear Congruence Equations and Chinese Remainder Theorem

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9 questions

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6 sample questions

Question 1.
What are the conditions under which a linear congruence has a unique solution?
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What do we mean by the coefficients being coprime?
Question 2.
Solve the linear congruence 4x ≡ 2 (mod 6).
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Check if a and n share common factors.
3Question 3.
What does it mean for two numbers to be coprime?
- They have no common divisors
- They are equal
- They are both prime
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Think about the GCD definition.
4Question 4.
True or False: The Chinese Remainder Theorem can find solutions for any moduli.
- True
- False
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Consider the requirements for CRT to work.
Question 5.
Solve the system of congruences: x ≡ 1 (mod 2), x ≡ 2 (mod 3), x ≡ 3 (mod 4). Show your work and verify all solutions.
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Break down each congruence systematically.
Question 6.
Apply the Extended Euclidean Algorithm to determine the inverse of 14 modulo 33, then solve 14x ≡ 11 (mod 33).
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Look for steps in the algorithm outlining the GCD.

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