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Question Number 187373 by Shrinava last updated on 16/Feb/23

$$\mathrm{Solve}\mathrm{for}\mathrm{natural}\mathrm{numbers}:$$$$31+\underset{\mathbf{k}=1}{\sum ^{\mathbf{n}}}(\left(\begin{array}{c}\mathrm{n}\\ \mathrm{k}\end{array}\right)\cdot \underset{\mathbf{m}=1}{\sum ^{\mathbf{n}}}{\mathrm{m}}^{\mathbf{n}-\mathbf{k}})={31}^{30}$$

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