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?
This is called a Quine:
A quine is a computer program which takes no input and produces a copy of its own source code as its only output. The standard terms for these programs in the computability theory and computer science literature are self-replicating programs, self-reproducing programs, and self-copying programs.
A quine is a fixed point of an execution environment, when the execution environment is viewed as a function. Quines are possible in any Turing complete programming language, as a direct consequence of Kleene's recursion theorem. For amusement, programmers sometimes attempt to develop the shortest possible quine in any given programming language.
Source: Wikipedia