Is there a way to solve diophantine equation of form $x^4+4y^4=n$ where $x,y$ are integers, and $n$ is large RSA modulus of size about 1024 bits?
$x^4+4y^4=n$ - it's Sophie Germain identity, which can be factored into
$$(x^2 + 2xy + 2y^2)(x^2 - 2xy + 2y^2) = ((x+y)^2+y^2)((x-y)^2+y^2).$$
Does that equation allow to factorize $n$ (better than brute-force n^1/4) or decrypt given ciphertext?
[It was last year ctf task(2017 asis, Sofies Verden), but there is no solution available for it]