I am trying to find out if there exists a language, which is recursively enumerable but not recursive, but which wouldn't also use Gdel's number or any other kind of Turing machine description in its definition. The language should be possible to somehow easily describe. (Easily being purely subjective, I know.)But each one I try to construct is either recursive or not recursively enumerable.
Recursively enumerable, non-recursive language without using Gdel's number
fl.formal languages;examples
Diophantine equations with a solution