Solve $ x^2+4=y^d$ in integers with $d\ge 3$ 
Find all triples of integers $(x,y,d)$ with $d\ge 3$ such that $x^2+4=y^d$.

I did some advance in the problem with Gaussian integers but still can't finish it. The problem is similar to Catalan's conjecture.
NOTE: You can suppose that $d$ is a prime.
Source: My head

See a similar question that I asked recently: Nontrivial Rational solutions to $y^2=4 x^n + 1$
This question might also be related to Fermat's Last Theorem.
