Question

Find a pair of integers x and y such that 61x + 41y = gcd(61, 41).

a. (1, 1)
b. (2, -3)
c. (0, 1)
d. (-1, 2)

Answer 1

The pair of integers x and y that satisfy the equation 61x + 41y = gcd(61, 41) is (-1, 2). Hence the correct answer is option D

Step-by-step explanation:

The given equation is 61x + 41y = gcd(61, 41). We can find the gcd(61, 41) by using the Euclidean algorithm. By applying the steps of the Euclidean algorithm, we find that the gcd(61, 41) = 1.

To find a pair of integers x and y that satisfies the equation, we can use the extended Euclidean algorithm. The extended Euclidean algorithm will give us the values of x and y that solve the equation. In this case, the pair of integers x and y that satisfies the equation is (-1, 2).

Hence the correct answer is option D