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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a linear congruence. Give an example.
💡 Hint: Remember the format of the equation.
Question 2
Easy
What does it mean for two integers to be co-prime?
💡 Hint: Think about their divisibility.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the Chinese Remainder Theorem guarantee?
- No solutions
- Unique solution modulo the product of moduli
- Multiple solutions within bounds
💡 Hint: Think about how CRT resolves multiple equations.
Question 2
True or False: If two integers are co-prime, they have a common divisor greater than 1.
- True
- False
💡 Hint: Consider the definition;
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that if a system of n linear congruences has a solution, there is a unique solution modulo the product of the moduli.
💡 Hint: Incorporate proof techniques like induction and explore implications of congruences.
Question 2
Given the numbers 10, 12, and 15 with a known sum, find numbers congruent to each, ensuring the CRT principles are satisfied.
💡 Hint: Break down the system and consider pairwise co-primality.
Challenge and get performance evaluation