9.28.2023
Question 1: Which one of the following Diophantine Equations is not solvable over the integers?
(3 points)
A. $3x + 6y + 9z = 24$
B. $2x + 8y + 4z = 94$
C. $4x + 8y+ 12z = 68$
D. $5x + 10y + 15z = 127$
Answer
D. $5x + 10y + 15z = 127$Question 2: Given that $\text{gcd}(3,17) = 1$, which of the following equations is not solvable over the integers?
(3 points)
A. $3x + 17y = 1$
B. $6x + 34y = 2$
C. $17x + 3y = 1$
D. $3x + 18y = 17$
Answer
D. $3x + 18y = 17$Question 3: Suppose you are asked to solve the Diophantine equation $3x +7y = 41$ over the natural numbers. Consider the parameterized equation $41 = 3(-82+7k) + 7(41-3k)$ for all integers $k$. Which of the following choices for $\mathbf{k}$ generates an acceptable solution for the Diophantine equation?
(3 points)
A. $11$
B. $13$
C. $14$
D. $15$