Practice Verifying the Solution - 10.8 | 10. Linear Congruence Equations and Chinese Remainder Theorem | Discrete Mathematics - Vol 3
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Verifying the Solution

10.8 - Verifying 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.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the solution for the linear congruence 4x ≡ 2 (mod 6)?

💡 Hint: Divide both sides by 2 after checking GCD.

Question 2 Easy

If 5x ≡ 10 (mod 15), what are possible values of x?

💡 Hint: What happens when you divide both sides by 5?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does it mean for a and N to be coprime when solving linear congruences?

They share a common divisor.
Their GCD is 1.
They are both even.

💡 Hint: Recall the definition of coprime.

Question 2

True or False: Every linear congruence has a unique solution.

True
False

💡 Hint: Consider the structure of modular arithmetic.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given five different congruences x ≡ 1 (mod 5), x ≡ 2 (mod 6), x ≡ 3 (mod 7), x ≡ 4 (mod 8), and x ≡ 5 (mod 9), determine the unique solution modulo the product of these moduli.

💡 Hint: Start solving each congruence stepwise using pairwise relationships.

Challenge 2 Hard

Find the multiplicative inverse of 15 modulo 26. Show each step.

💡 Hint: Remember the steps to apply the algorithm carefully.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.