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Is there a problem that has only a recursive solution?
Can every recursion be converted into iteration?
“Necessary” Uses of Recursion in Imperative Languages
Is there a problem that has only a recursive solution, that is, a problem that has a recursive solution, but an iterative solution has yet to be found, or better yet, has proven to be non-existing (obviously, this is not a tail-recursion)?
The Ackermann function cannot be expressed without recursion
edit: As noted in another answer, this is incorrect.