solequa

solequa.py

import math
def isPosInt(x):
    return x >= 0 and x.is_integer()


def findABs(n):
    start = 2 if isPosInt(n / 2) else 1
    limit = int(math.sqrt(n)) + 1
    solutions = []
    step = 2
    for x in range(start, limit, step):
        y = n / x
        if isPosInt(y):
            solutions.append([int(x), int(y)])
    return solutions


def sol_equa(n):
    abs = findABs(n)
    solutions = []
    for ab in abs:
        a = ab[0]
        b = ab[1]
        y = (b - a) // 4
        x = (a + b) // 2
        isSolution = x ** 2 - 4 * y ** 2 == n
        if isSolution:
            solutions.append([int(x), int(y)])

    return solutions