Can 13477627276039606281933936961 be expressed as a sum of two fourth powers?

Question

Is 13477627276039606281933936961 the sum of two fourth powers? I suspect that this number is the sum of two fourth powers. Can anyone use Wolfram Mathematica or SAGE to check whether this number is the sum of two fourth powers ?

Answer 1

The number is small enough to brute force.

Edit: fixed number

import gmpy2
N = 13477627276039606281933936961

for x in range(1, int((N**0.25)/2)+1):
    if gmpy2.is_square(N - x**4):
        print(x, (N-x**4)**0.25)

Output:

3330955 10749966.0

>>> 3330955**4 + 10749966**4 == 13477627276039606281933936961
True