Practice Chinese Remainder Theorem (crt) (10.3) - Linear Congruence Equations and Chinese Remainder Theorem

Practise this section

9 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is a linear congruence? Provide an example.
Show hintHide hint
Look for the standard form.
Question 2.
How many solutions does the linear congruence 4x ≡ 8 (mod 12) have?
Show hintHide hint
Consider all values that satisfy the equation.
3Question 3.
What is a linear congruence?
Show hintHide hint
Think of modular arithmetic.
4Question 4.
True or False: The Chinese Remainder Theorem guarantees multiple solutions for all systems of linear congruences.
- True
- False
Show hintHide hint
Recall the uniqueness condition.
Question 5.
Find all integer solutions for the system: x ≡ 1 (mod 4), x ≡ 3 (mod 5), and x ≡ 2 (mod 7).
Show hintHide hint
Start with calculating the larger modulus.
Question 6.
Determine the implications of changing one modulus in a set of congruences. For instance, replace mod 5 with mod 6.
Show hintHide hint
Evaluate how congruences relate to divisibility.

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