Linear Congruences and GCD Problems
Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Practice Problem
•
Hard
Thomas White
FREE Resource
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13 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a linear congruence?
An equation of the form ax + b = c
A system of linear equations
A congruence of the form ax ≡ b (mod n)
A polynomial equation of degree 2
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Under what condition does a linear congruence have a solution?
When a is greater than b
When n is a prime number
When gcd(a, n) divides b
When a and b are coprime
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the first example, what is the gcd of 9 and 15?
1
2
5
3
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why can we cancel the common factor in the congruence 3x ≡ 2 (mod 5)?
Because 3 divides 2
Because 5 is a prime number
Because 3 is a prime number
Because gcd(3, 5) = 1
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first solution for x in the congruence 3x ≡ 2 (mod 5)?
0
1
3
4
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How many incongruent solutions does the congruence 9x ≡ 6 (mod 15) have?
3
1
2
4
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of x when t = 1 in the solution of 9x ≡ 6 (mod 15)?
19
14
9
4
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