Test: Algebra - 1 - Software Development MCQ

In linear diophantine equations of the form ax + by = c, where a, b, and c are integers, which of the following is true?

Which of the following is an example of a linear diophantine equation?

What will be the output of the code snippet?
a = 5
b = 3
c = a + b
print(c)

What will be the output of the code snippet?
a = 10
b = 2
c = a / b
print(c)

What will be the output of the code snippet?
a = 10
b = 3
c = a % b
print(c)

What will be the output of the following code snippet?
def binary_exponentiation(a, n):
    if n == 0:
        return 1
    elif n % 2 == 0:
        x = binary_exponentiation(a, n // 2)
        return x * x
    else:
        x = binary_exponentiation(a, (n - 1) // 2)
        return a * x * x

result = binary_exponentiation(2, 5)
print(result)

What will be the output of the following code snippet?
def gcd(a, b):
    if b == 0:
        return a
    else:
        return gcd(b, a % b)

result = gcd(21, 14)
print(result)

What will be the output of the following code snippet?
def sieve_of_eratosthenes(n):
    prime = [True] * (n + 1)
    p = 2
    while p * p <= n:
        if prime[p] == True:
            for i in range(p * p, n + 1, p):
                prime[i] = False
        p += 1

    primes = []
    for p in range(2, n + 1):
        if prime[p]:
            primes.append(p)
    return primes

result = sieve_of_eratosthenes(20)
print(result)

What will be the output of the following code snippet?
def linear_diophantine(a, b, c):
    g = gcd(a, b)
    if c % g != 0:
        return "No solution exists."
    x0, y0 = extended_euclidean(a, b)
    x = x0 * (c // g)
    y = y0 * (c // g)
    return x, y

result = linear_diophantine(5, 7, 16)
print(result)

What will be the output of the following code snippet?

def binary_exponentiation(a, n):
    if n == 0:
        return 1
    elif n % 2 == 0:
        x = binary_exponentiation(a, n // 2)
        return x * x % 1000000007
    else:
        x = binary_exponentiation(a, (n - 1) // 2)
        return a * x * x % 1000000007

result = binary_exponentiation(2, 10)
print(result)

What will be the output of the following code snippet?
def gcd(a, b):
    if b == 0:
        return a
    else:
        return gcd(b, a % b)

result = gcd(24, 36)
print(result)

What will be the output of the following code snippet?

def linear_diophantine(a, b, c):
    g = gcd(a, b)
    if c % g != 0:
        return "No solution exists."
    x0, y0 = extended_euclidean(a, b)
    x = x0 * (c // g)
    y = y0 * (c // g)
    return x, y

result = linear_diophantine(3, 5, 8)
print(result)