num-square-differences.py

import numpy as np
from itertools import combinations

primes = [2, 2, 2, 5, 5, 7]
number = 1400
assert np.prod(primes) == number  # sanity check

observed_sets = set()
n_hips = 0

for i in range(1, len(primes)):
    for subset in combinations(primes, i):
        x = np.prod(subset)
        y = number // x

        if x < y and x not in observed_sets :
            observed_sets.add(x)

            if (y - x) % 2 == 0:
                b = (y - x) // 2
                a = b + x
                assert (a**2 - b**2) == number, a**2 - b**2  # sanity check
                print(f"a={a}, b={b}")
                n_hips += 1

print(f"Number of hips: {n_hips}")