Question

find the multiplicative inverse of 32(mod 101). answer must range from 0 to 100

Answer 1

Searching one by one is very tedious, instead I have used python-program to solve it, which is as follows

# Python program to find
# modular inverse using extended
# Euclid algorithm
# Returns modulo inverse of a with
# respect to m using extended Euclid
def modInverse(a, m):
    m0 = m
    y = 0
    x = 1
    if (m == 1):
        return 0
    while (a > 1):
        # q is quotient
        q = a // m
        t = m
        # m is remainder now, process
        # same as Euclid's algo
        m = a % m
        a = t
        t = y
        # Update x and y
        y = x - q * y
        x = t
        # Make x positive
    if (x < 0):
        x = x + m0
    return x
# Driver program to test above function
a = 32
m = 101
print("Modular multiplicative inverse is",
      modInverse(a, m))

The out put is as follows
Modular multiplicative inverse is 60.

Now manually we can verify 32*60(mod 101)= 1.