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I just cast a vote to undelete. The question was deleted by the poster (Lisa R.), for reasons unknown. Gerhard Paseman recommended that the title be made more specific for some reason (the title was completely fine in my opinion), and perhaps she took that to heart and is planning to ask another question.
The question is now open, for those wondering.
Not completely convinced regarding the title-theory but one never knows. For the record, it was me who changed the title (already).
The original title (on which gpr) commented was "Matrices over $\mathbb{Z}_n$", which is not a bad title, but then I think the current one (the one essentially suggested by gpr and made by me just taking the first line of the question basically) "Number of idempotent $n \times n$ matrices over $\mathbb{Z}_m" is quite a bit more informative (besides the usage of the letter n now being the same in title and body).
Thanks for clarifying, quid. I had thought that was the original title.
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