n = 100
squareOfSum = sumOfSquares = 0
squareOfSum = 0


# based on a simple internet search
# I found you can find the sum
# of an arithmetic series with
#    Sn = n/2(a1 + an)

squareOfSum =  n/2 * (1 + n)

squareOfSum = squareOfSum ** 2

#with another internet search 
#I found you can get the sum of squares
#with the following
# ((n)(n+1)(2n+1)) / 6

sumOfSquares = (n * (n + 1) * (2 * n + 1)) / 6

#get the difference between the two
difference = squareOfSum - sumOfSquares

print "The square of the sum is  %d" % (squareOfSum,)
print "The sum of squares is  %d" % (sumOfSquares,)
print "The difference is %d" % (difference,) 

#the following code solves it the 
#more obvious way  but just 
#adding up the numbers in a loop
#requires no math prowess, but 
#it's slower

squareOfSum = 0
sumOfSquares = 0
i = 1

while i <= n:
    sumOfSquares += i**2
    squareOfSum += i
    i += 1
    
squareOfSum = squareOfSum ** 2

difference = squareOfSum - sumOfSquares

print "The square of the sum is  %d" % (squareOfSum,)
print "The sum of squares is  %d" % (sumOfSquares,)
print "The difference is %d" % (difference,)