Can a program output a copy of itself

Question

I think this might be a classic question but I am not aware of an answer. Can a program output a copy of itself, and, if so, is there a short program that does this?

Answer 1

This is indeed a classic question!

Beyond the existence of specific quines, an important result in computability theory is that for any function you might want to compute, there exists a program that "knows its own program text", i.e. that could print itself if desired. This theorem is called Kleene's second recursion theorem.