Practice Finding Solutions in a Specific Range - 10.9 | 10. Linear Congruence Equations and Chinese Remainder Theorem | Discrete Mathematics - Vol 3
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Finding Solutions in a Specific Range

10.9 - Finding Solutions in a Specific Range

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the solution to 2x ≡ 4 (mod 3)?

💡 Hint: Find the integer value of `x` satisfying the equation.

Question 2 Easy

Determine if 1x ≡ 5 (mod 10) has solutions, and if so, provide one.

💡 Hint: Solve the equation normally then check for modulo.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What kind of equations are expressed as ax ≡ b (mod N)?

Linear equations
Linear Congruences
Quadratic equations

💡 Hint: Look for terms that involve modulus.

Question 2

True or False: Every linear congruence has at least one solution.

True
False

💡 Hint: Consider the structure of congruences.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that if ax ≡ b (mod N) has a solution for GCD(a, N) = d, then it implies a system of equations.

💡 Hint: Use properties of divisors and modular arithmetic.

Challenge 2 Hard

For three congruences x ≡ 1 (mod 6), x ≡ 2 (mod 15), and x ≡ 3 (mod 10), find all solutions up to M.

💡 Hint: Work through each congruence step to consolidate solutions.

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