@math
Hi! I am currently working on an open Diophantine equation listed in a publication by Dr Bogdan Grechuk: y^3 + xy = x^4 + 4. The question if any integer solutions exist eludes brute force attempts even with scripts in systems such as SageMath. Empirical work suggests there may be no solutions. I have been trying to prove by various approaches that no integer solutions exist. Dr Gerchuk gave critical feedback on my first two approaches but I am hoping to get more informal feedback or even collaboration on this before I send it to him a third time.
Here is the Overleaf link to the project and I am open to also share a link to edit and possibly coauthor if anyone is interested in helping get this case closed or to lay it to rest.
https://www.overleaf.com/read/ncqwpfxzkqfr#5621d2