Practice Discrete Mathematics - 11.1 | 11. Uniqueness Proof of the CRT | Discrete Mathematics - Vol 3
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Discrete Mathematics

11.1 - Discrete Mathematics

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Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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;

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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