Codewars - Sum(1 to n) - a - b = a * b

'''
A friend of mine takes a sequence of numbers from 1 to n (where n > 0).
Within that sequence, he chooses two numbers, a and b.
He says that the product of a and b should be equal to the sum of all numbers in the sequence, excluding a and b.
Given a number n, could you tell me the numbers he excluded from the sequence?
'''

# Function 1
def removeABfromSum(n):
    if n <= 1 or n != int(n):
        print("Error while using the function '" + removeABfromSum.__name__ + "'")
        return -1000000
    SUM = n * (n + 1) / 2
    solA = -1000
    solB = -1000
    for a in range(1, n+1):
        b = (SUM - a) / (a + 1)
        if b == int(b) and b > a and b <= n:
            # That means that the pair (a,b) is a solution of this problem
            # The value of a and b remain! So, I will break the loop in order to gain time
            solA = int(a)
            solB = int(b)
            break
    return int(SUM), solA, solB


# Function 2
def prettyPrint(n):
    SUM, solA, solB = removeABfromSum(n)
    if solA == -1000 and solB == -1000:
        print("n = " + str(n) + " ----> sum = " + str(SUM) + " ----> No solutions a,b")
    else:
        print("n = " + str(n) + " ----> sum = " + str(SUM) + " ----> a = " + str(solA) + ", b = " + str(solB))


# MAIN FUNCTION
nList = list(range(2, 101))
for n in nList:
    prettyPrint(n)