Let $m, n \in N$ and $\operatorname{gcd}(2, n)=1$. If
$30\left(\begin{array}{l}30 \\ 0\end{array}\right)+29\left(\begin{array}{l}30 \\ 1\end{array}\right)+\ldots+2\left(\begin{array}{l}30 \\ 28\end{array}\right)+1\left(\begin{array}{l}30 \\ 29\end{array}\right)=\mathrm{n} \cdot 2^{\mathrm{m}}$, then $\mathrm{n}+\mathrm{m}$ is equal to
(Here $\left(\begin{array}{l}\mathrm{n} \\ \mathrm{k}\end{array}\right)={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{k}}$ )
$30\left({ }^{30} \mathrm{C}_{0}\right)+29\left({ }^{30} \mathrm{C}_{1}\right)+\ldots+2\left({ }^{30} \mathrm{C}_{28}\right)+1\left({ }^{30} \mathrm{C}_{29}\right)$
$=30\left({ }^{30} \mathrm{C}_{30}\right)+29\left({ }^{30} \mathrm{C}_{29}\right)+\ldots \ldots+2\left({ }^{30} \mathrm{C}_{2}\right)+1\left({ }^{30} \mathrm{C}_{1}\right)$
$=\sum_{\mathrm{r}=1}^{30} \mathrm{r}\left({ }^{30} \mathrm{C}_{\mathrm{r}}\right)$
$=\sum_{\mathrm{r}=1}^{30} \mathrm{r}\left(\frac{30}{\mathrm{r}}\right)\left({ }^{29} \mathrm{C}_{\mathrm{r}-1}\right)$
$=30 \sum_{\mathrm{r}=1}^{30}{ }^{29} \mathrm{C}_{\mathrm{r}-1}$
$=30\left({ }^{29} \mathrm{C}_{0}+{ }^{29} \mathrm{C}_{1}+{ }^{29} \mathrm{C}_{2}+\ldots+{ }^{29} \mathrm{C}_{29}\right)$
$=30\left(2^{29}\right)=15(2)^{30}=\mathrm{n}(2)^{\mathrm{m}}$
$\therefore \mathrm{n}=15, \mathrm{~m}=30$
$\mathrm{n}+\mathrm{m}=45$
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