Solution Exercise 62: Python Algorithm that test whether a given integer is sum of two perfetc squares

Exercise 62 || Solution

Create a  Python algorithm that tests whether a given integer is sum of two perfect squares. Example the integer n = 13 is sum of two perfects squares 13 = 2 ^ 2 + 3 ^ 2.

Solution

n = int(input("Enter value of integer n : "))
# initialize solutions
a = 0
b = 0
# initialize counter to test the existence of possible solutions
counter = 0

for i in range(1, n+1):
    for j in range(1,n+1):
        if i**2 + j**2 == n:
            a = i
            b = j
            counter = counter + 1 
            break
if ( counter > 0):
    print("The integer " , n , " is sum of two perfects squares :" 
          , n , " = ", a, "^2" ," + " , b ,"^2") 
else:
    print("The integer " , n , " is not sum of two perfects squares !")
        
# Testing algorithm for n = 13
# The output is : The integer  13  is sum of two perfects squares : 13  =  3 ^2  +  2 ^2