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Note by Nicholas Fortino 5 years, 8 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 a simple application of Wilson's Theorem.

First, note that \(9! \equiv -1\) (mod \(71\)).

Then, since \(71\) is a prime, by Wilson's Theorem,

\(70! \equiv -1\) (mod \(71\)).

But \(70! \equiv 61! (62)(63)(64)...(70) \equiv 61! (-9)(-8)(-7)...(-1)\) \( \equiv -61!(9!) \equiv 61! \) (mod \(71\)).

But \(70! \equiv -1\) (mod \(71\)).

So \(61! \equiv 70! \equiv -1\) (mod \(71\)).

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Oh I see why I was looking at it the wrong way. Nice proof Zi song :)

I'm not that great at modulus arithmetic but how can 61!= -1 mod(7) ? Doesn't that mean that it is smaller than 7 ?

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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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TopNewestThis is a simple application of Wilson's Theorem.

First, note that \(9! \equiv -1\) (mod \(71\)).

Then, since \(71\) is a prime, by Wilson's Theorem,

\(70! \equiv -1\) (mod \(71\)).

But \(70! \equiv 61! (62)(63)(64)...(70) \equiv 61! (-9)(-8)(-7)...(-1)\) \( \equiv -61!(9!) \equiv 61! \) (mod \(71\)).

But \(70! \equiv -1\) (mod \(71\)).

So \(61! \equiv 70! \equiv -1\) (mod \(71\)).

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Oh I see why I was looking at it the wrong way. Nice proof Zi song :)

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I'm not that great at modulus arithmetic but how can 61!= -1 mod(7) ? Doesn't that mean that it is smaller than 7 ?

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