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# Perfect Power??

Can there exist a number of the form $$xyxyxy$$ which is a perfect power???

$$\textbf{Details and Assumptions:}$$A perfect power means a number of the form $$p^{k}$$ where $$p$$ is an integer.

3 years, 2 months ago

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$$\overline{xyxyxy}$$

$$= \overline{xy} \times 10101$$

$$= \overline{xy} \times 3 \times 7 \times 13 \times 37$$

This implies that for $$\overline{xyxyxy}$$ to be a perfect power, $$\overline{xy}$$ must contain a factor of $$3 ,7,13$$ and $$37$$ which is not possible as it will cause it to be greater than 2 digits. · 3 years, 2 months ago