Python Program for Number of solutions to Modular Equations

# Python Program to find number of possible
# values of X to satisfy A mod X = B
import math

# Returns the number of divisors of (A - B)
# greater than B
def calculateDivisors (A, B):
    N = A - B
    noOfDivisors = 0
    
    a = math.sqrt(N)
    for i in range(1, int(a + 1)):
        # if N is divisible by i
        if ((N % i == 0)):
            # count only the divisors greater than B
            if (i > B):
                noOfDivisors +=1
                
            # checking if a divisor isnot counted twice
            if ((N / i) != i and (N / i) > B):
                noOfDivisors += 1;
                
    return noOfDivisors
    
# Utility function to calculate number of all
# possible values of X for which the modular
# equation holds true
    
def numberOfPossibleWaysUtil (A, B):
    # if A = B there are infinitely many solutions
    # to equation or we say X can take infinitely
    # many values > A. We return -1 in this case
    if (A == B):
        return -1
        
    # if A < B, there are no possible values of
    # X satisfying the equation
    if (A < B):
        return 0
        
    # the last case is when A > B, here we calculate
    # the number of divisors of (A - B), which are
    # greater than B
    
    noOfDivisors = 0
    noOfDivisors = calculateDivisors;
    return noOfDivisors
        
    
# Wrapper function for numberOfPossibleWaysUtil()
def numberOfPossibleWays(A, B):
    noOfSolutions = numberOfPossibleWaysUtil(A, B)
    
    #if infinitely many solutions available
    if (noOfSolutions == -1):
        print ("For A = " , A , " and B = " , B
                , ", X can take Infinitely many values"
                , " greater than " , A)
    
    else:
        print ("For A = " , A , " and B = " , B
                , ", X can take " , noOfSolutions
                , " values")
# main()
A = 26
B = 2
numberOfPossibleWays(A, B)

A = 21
B = 5
numberOfPossibleWays(A, B)

# Contributed by _omg

Output:

For A = 26 and B = 2, X can take 6 values
For A = 21 and B = 5, X can take 2 values