Python Classic Exercise 1: An integer, which plus 100 is a complete square number, plus 168 is a complete square number, what is the number?

Python Classic Exercises

The answers that can be searched online are:

 
 
for i in range(1,85):
    if 168 % i == 0:
        j = 168 / i;
        if  i > j and (i + j) % 2 == 0 and (i - j) % 2 == 0 :
            m = (i + j) / 2
            n = (i - j) / 2
            x = n * n - 100
            print(x)

The output answers are:

-99
21
261
1581

But in fact, four figures are not in accordance with the conditions of +100 and +168, which are still the full square number;

The correct code is as follows:

 
 
import math
n = 0
count = 0
while True:
    first = n + 100
    second = n + 168
    first_sqrt = int(math.sqrt(first))
    second_sqrt = int(math.sqrt(second))
    if (first_sqrt*first_sqrt == first) and (second_sqrt*second_sqrt == second):
        print(n)
        break
    n = n + 1

The correct answer is only one:

156

Python Classic Exercise 1: An integer, plus 100 is a complete square number, plus 168 is a complete square number, what is the number?