# 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.

4 years, 1 month ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

$$\overline{xyxyxy}$$

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

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

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.

- 4 years, 1 month ago

Nice job!

- 4 years, 1 month ago