def fermat_factor(n):
    assert n % 2 != 0  # Odd integers only

    a = gmpy2.ceil(gmpy2.sqrt(n))
    b2 = gmpy2.square(a) - n
    while not is_square(b2):
        a += 1
        b2 = gmpy2.square(a) - n

    factor1 = a + gmpy2.sqrt(b2)
    factor2 = a - gmpy2.sqrt(b2)
    return int(factor1), int(factor2)

def is_square(n):
    root = gmpy2.sqrt(n)
    return root % 1 == 0  # '4.0' will pass, '4.1212' won't

factor1 = a + gmpy2.sqrt(b2)
factor2 = a - gmpy2.sqrt(b2)

factor1 = factor2 = gmpy2.sqrt(b2)
factor1 += a
factor2 -= a