Practice Application Of Chinese Remainder Theorem (11.2.6)

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6 sample questions

Question 1.
What is the Chinese Remainder Theorem?
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Consider its relation to moduli.
Question 2.
Define coprime numbers.
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Think of prime numbers.
3Question 3.
What is guaranteed by the Chinese Remainder Theorem?
- No solution exists
- A unique solution exists
- Multiple solutions exist
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Think about the uniqueness in systems of equations.
4Question 4.
True or False: If two numbers are congruent mod m and m is prime, they are equal.
- True
- False
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Consider the possibilities outside of congruence.
Question 5.
Prove that the CRT can be extended to more than two moduli.
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Think about the relationships of congruences.
Question 6.
If 17 and 19 are coprime moduli, find a number less than 323 that is congruent to 5 mod 17 and congruent to 12 mod 19.
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Calculate the respective products and their inverses.

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