Practice Linear Congruence Equations And Chinese Remainder Theorem (10) - Linear Congruence Equations and Chinese Remainder Theorem

Practice: Linear Congruence Equations and Chinese Remainder Theorem

Lesson 10Linear Congruence Equations and Chinese Remainder Theorem

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8 questions

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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What does the notation a ≡ b (mod N) mean?
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Think about the definition of congruence.
Question 2.
If x ≡ 3 (mod 5), what could be a value of x?
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Find such numbers by adding multiples of 5.
3Question 3.
What is the condition for using the extended Euclidean algorithm?
- GCD(a
- N) = 1
- GCD(a
- N) > 1
- a and N are both 0
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What condition does the existence of an inverse require?
4Question 4.
True or False: The Chinese Remainder Theorem guarantees a unique solution for any set of congruences.
- True
- False
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Think about the conditions of the theorems discussed.
Question 5.
Using the Chinese Remainder Theorem, solve for x in the system: x ≡ 1 (mod 4), x ≡ 3 (mod 5), x ≡ 2 (mod 7).
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Determine the product of moduli and work through the steps of CRT.
Question 6.
Show that x ≡ 5 (mod 15) has infinitely many solutions, and list at least three.
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Use the general formula for solutions in linear congruences.

4 more questions in this section. Enroll free to practise them all.