
Diophantine Equations and Number Theory

Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Hard

Thomas White
FREE Resource
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11 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the central problem in number theory discussed in the video?
Finding all real number solutions to equations
Solving Diophantine equations
Calculating complex number solutions
Understanding algebraic expressions
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What type of solutions are we interested in for Diophantine equations?
Fractional solutions
Integer solutions
Complex number solutions
Real number solutions
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How does solving equations in number theory differ from algebra?
Number theory focuses on particular solutions
Algebra focuses on integer solutions
Algebra focuses on complex solutions
Number theory focuses on all solutions
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the next step in complexity after solving single-variable Diophantine equations?
Solving equations with three variables
Solving equations with two variables of degree one
Solving quadratic equations
Solving equations with fractional coefficients
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the specific case of Diophantine equations discussed in the video?
ax + by = gcd(a, b)
ax + by = c
ax + by = a + b
ax + by = 0
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the example problem used to illustrate the solution process?
47x + 30y = 1
47x + 30y = 0
47x + 30y = 47
47x + 30y = 30
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What algorithm is used to find the greatest common divisor in the example?
Simplex algorithm
Euclidean algorithm
Newton's method
Gaussian elimination
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