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The factors of $72$ are $1,2,3,4,6,8,9,12,18,24,36,72$. The factors can be organized as such:

  • $m=1,2,3,4,6,8$, and
  • $n=72,36,24,18,12,9$.

Knowing the symmetric properties and that the $12$ factors exist. Is there a way to rewrite $n$ as a function of $m$ without actually diving $72$ by $m$? I tried adding and subtracting $m$ and $n$ to find a pattern as to get a clue as to what value the other might be without actually dividing.

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  • $\begingroup$ The defining relation between $m$ and $n$ is $mn=72$. There is no polynomial expression of $m$ in terms of $n$ nor vice-versa because division cannot be done by addition and multiplication. $\endgroup$ – lhf Sep 26 '13 at 16:16

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