Problem #931

 931 For how many positive integers $m$ does there exist at least one positive integer n such that $m \cdot n \le m + n$? $\mathrm{(A) \ } 4\qquad \mathrm{(B) \ } 6\qquad \mathrm{(C) \ } 9\qquad \mathrm{(D) \ } 12\qquad \mathrm{(E) \ }$ infinitely many This problem is copyrighted by the American Mathematics Competitions.
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