10.6 - Finding a Special Linear Combination for the Solution
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
Solve the linear congruence 4x ≡ 2 (mod 10).
💡 Hint: Try dividing both sides if GCD of coefficients is 1.
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.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the term 'linear congruence' refer to?
💡 Hint: Think about the context of modular operations.
True or False: The Chinese Remainder Theorem guarantees a unique solution modulo the product of the pairwise co-prime moduli.
💡 Hint: Recall the main properties of CRT.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
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?
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.