Question

有多少个正整数 $m$ 满足：存在至少一个正整数 $n$ ，使得 $m \cdot n \le m + n$ ？

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

$4$

$6$

$9$

$12$

无穷多个

infinitely many

取 $n = 1$ ，不等式变为 $m \le m + 1$ ，这对每个正整数 $m$ 都成立。

所以每个正整数 $m$ 都满足条件，共有无穷多个。

因此，正确答案是 E。

Taking $n = 1,$ the inequality becomes $m \le m + 1,$ which holds for every positive integer $m.$

So every positive integer $m$ works, and there are infinitely many.

Thus, the correct answer is E.