sum-of-cubes.py

# This algorithm defines whether user's integer input is representable as a sum of 2 cubes
# or not. If number is representable, it finds all the combinations

a = input("Enter a natural number: ")
i = 0
fails = 0
deny = None
print()

for i in a:
    if i == "." or i == "-":
        deny = True
        break
    else:
        deny = False

while deny:
    fails += 1
    a = input("Enter a NATURAL number: ")
    for i in a:
        if i == "." or i == "-":
            deny = True
            break
        else:
            deny = False

if fails > 0:
    print()

a = int(a)

n1 = 1
counter = 0
isRepresentable = None

while n1 <= round(((4 * a) ** (1/3)) * 0.5) and a - (n1 ** 3) > 0:
    n2 = (a - (n1 ** 3)) ** (1/3)
    n3 = round(n2)
    if n1 ** 3 + n3 ** 3 == a and n3 >= n1:
        print("[!] Result found: ", n3, "³ + ", n1, "³ = ", a, sep="")
        n1 += 1
        counter += 1
        isRepresentable = True
    else:
        n1 += 1

if not isRepresentable:
    print("[!] The number has no representation as a sum of 2 cubes")
elif isRepresentable and counter > 1:
    print()
    print("(!) Combinations:", counter)