11.1 - Discrete Mathematics
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
Define a linear congruence. Give an example.
💡 Hint: Remember the format of the equation.
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
What does the Chinese Remainder Theorem guarantee?
💡 Hint: Think about how CRT resolves multiple equations.
True or False: If two integers are co-prime, they have a common divisor greater than 1.
💡 Hint: Consider the definition;
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
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.
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.