Question

Python

We say that a pair of positive integers ?,? is special if ? − ? = 10 and both ? and ? can be represented as a sum of two squares. For example, the pair (18,8) is special since 18 − 8 = 10, 18 = 3^2 + 3^2, and 8 = 2^2 + 2^2. Write a program that prints all special pairs (?,?) with 1 ≤ ?,? ≤ 100.

Answer 1

import math
def sum_of_square(n):
    a, b = 0, 0
    for i in range(1,n):
        remainder = n - i ** 2
        if remainder < 0: return False
        if remainder>0 and remainder ** 0.5 == math.ceil(remainder ** 0.5):
            return True


for y in range(1, 101):
    x = y + 10
    if sum_of_square(x) and sum_of_square(y):
        print('({},{})'.format(x, y))