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Prove that there does exist some integers \(n\) such that \( 3^{n}+3^{n-1}+3^{n-2}+......+3^{4}+3^{3}+3^{2}+3^{1}+3^{0}\) is a perfect square, or else define the \[\color{BLUE}{\huge{1000th}}\] smallest value of \(n\).

Note by Bryan Lee Shi Yang 3 years, 3 months ago

Easy Math Editor

*italics*

_italics_

**bold**

__bold__

- bulleted- list

1. numbered2. list

paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)

> 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"

2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

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...Sorry, note edited.

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You have mentioned it to be an integer. Other values will be 0,1,4

I am sorry, it should be a \(POSITIVE\) number.

It can be a perfect square. Smallest possible value of n will be -1.

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewest...Sorry, note edited.

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You have mentioned it to be an integer. Other values will be 0,1,4

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I am sorry, it should be a \(POSITIVE\) number.

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It can be a perfect square. Smallest possible value of n will be -1.

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