10.9 - Finding Solutions in a Specific Range
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Practice Questions
Test your understanding with targeted questions
What is the solution to 2x ≡ 4 (mod 3)?
💡 Hint: Find the integer value of `x` satisfying the equation.
Determine if 1x ≡ 5 (mod 10) has solutions, and if so, provide one.
💡 Hint: Solve the equation normally then check for modulo.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What kind of equations are expressed as ax ≡ b (mod N)?
💡 Hint: Look for terms that involve modulus.
True or False: Every linear congruence has at least one solution.
💡 Hint: Consider the structure of congruences.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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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