Practice Proof Strategy For Chinese Remainder Theorem (10.5) - Linear Congruence Equations and Chinese Remainder Theorem

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6 sample questions

Question 1.
What is a linear congruence?
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Think about what happens in usual algebra with variables.
Question 2.
State the Chinese Remainder Theorem.
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Consider how multiple conditions can coexist.
3Question 3.
What is a linear congruence?
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Focus on the equation format and its components.
4Question 4.
True or False: The Chinese Remainder Theorem guarantees multiple solutions in the range of moduli.
- True
- False
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Consider what 'unique' means in this context.
Question 5.
Prove that for any integers a, b, and N, if GCD(a, N) = d > 1, then the linear congruence ax ≡ b mod N has either no solutions or infinitely many solutions.
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Consider factors and multiples involved in the equation.
Question 6.
Using the Extended Euclidean Algorithm, find the solutions x for the congruence 15x ≡ 3 mod 30.
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Reduce the congruence to simpler terms using the GCD.

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