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.

Note by Eddie The Head
4 years, 1 month 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.

Siddhartha Srivastava - 4 years, 1 month ago

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Nice job!

Eddie The Head - 4 years, 1 month ago

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