Practice Finding a Special Linear Combination for the Solution - 10.6 | 10. Linear Congruence Equations and Chinese Remainder Theorem | Discrete Mathematics - Vol 3
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Solve the linear congruence 4x ≡ 2 (mod 10).

💡 Hint: Try dividing both sides if GCD of coefficients is 1.

Question 2

Easy

What is the multiplicative inverse of 3 mod 7?

💡 Hint: Find a number which, when multiplied by 3, gives a remainder of 1 when divided by 7.

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Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does the term 'linear congruence' refer to?

  • An algebraic equation
  • A system of equations
  • An equation under modular arithmetic

💡 Hint: Think about the context of modular operations.

Question 2

True or False: The Chinese Remainder Theorem guarantees a unique solution modulo the product of the pairwise co-prime moduli.

  • True
  • False

💡 Hint: Recall the main properties of CRT.

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Challenge Problems

Push your limits with challenges.

Question 1

Prove that the solutions for the linear congruence 12x ≡ 12 (mod 18) include infinite entries.

💡 Hint: How can you express x based on multiples of the reduced expression?

Question 2

Given three congruences x ≡ 4 (mod 7), x ≡ 5 (mod 9), and x ≡ 6 (mod 10), find the smallest x that satisfies them.

💡 Hint: Combine each congruence carefully, noting pairwise properties.

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