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Find all pairs \((m,n)\) of non-negative integers for which \[m^2+2\cdot 3^{n}=m \left(2^{n+1}-1\right)\]

Note by Akshat Sharda 1 year, 11 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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This is problem N2 (proposed by Austrilia) of the 51st IMO Shortlist (2010).

Official solution:

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What have you tried? What restrictions can we place on \(m\)?

I'm not able to get a start on problems like this.

Please tell me what approach should I take on problems like these.

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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

Sort by:

TopNewestThis is problem N2 (proposed by Austrilia) of the 51st IMO Shortlist (2010).

Official solution:Log in to reply

What have you tried? What restrictions can we place on \(m\)?

Log in to reply

I'm not able to get a start on problems like this.

Please tell me what approach should I take on problems like these.

Log in to reply