For how many positive integers $m,$ $1 \le m \le 1000,$ does there exist at least one positive integer $n$ such that $m \cdot n \le m + n$?
Question:
For how many positive integers $m,$ $1 \le m \le 1000,$ does there exist at least one positive integer $n$ such that $m \cdot n \le m + n$?
Answer:
Let's think step by step.

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For how many positive integers $m,$ $1 \le m \le 1000,$ does there exist at least one positive integer $n$ such that $m \cdot n \le m + n$?
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