New user? Sign up

Existing user? Sign in

can anyone help me in finding the remainder when \(3^{942}\) is divided by 2014?? I dont need answer just help!!!!! please.

Note by Gautam Sharma 3 years, 1 month 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}

Sort by:

\(\phi(2014)=936\)

And \(\gcd(3,2014)=1\)

By Euler-Fermat theorem we have \(3^{\phi(2014)}\equiv 3^{936}\equiv 1\mod 2014\)

\(\Rightarrow 3^{936}\times 3^6\equiv 3^{942}\equiv 729 \mod 2014\)

Log in to reply

I want to ask How to read it or interpret this like when we do 12/3=4 , we say when 12 is divided by 3 we get 4 as a quotient.How to read it?

\(12\equiv 1 \mod 11\)

is read as "12 congruent to 1 mod 11" or "12 equivalent to 1 mod 11"

I always use Euler's totient function since it reduces exponents into a fathomable number. (Though I still do not know the proof of the theorem, would be great if someone presents one)

U may find it here

please explain it or give another way please please.........

Sorry for my mistake I've now edited it. There's no other method to my knowledge. U can look up this theorem in the brilliant wiki.

@Aneesh Kundu – NO Problem. BTW IT WAS YOUR QUESTION. I got k=3 but was unable to get remainder.

@Aneesh Kundu – @GAUTAM SHARMA Check out Euler's Theorem in the Modular Arithmetic Wiki. That should provide you with explanations about how to approach problems like this.

@Calvin Lin – Thanks D);.

Problem Loading...

Note Loading...

Set Loading...

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:

TopNewest\(\phi(2014)=936\)

And \(\gcd(3,2014)=1\)

By Euler-Fermat theorem we have \(3^{\phi(2014)}\equiv 3^{936}\equiv 1\mod 2014\)

\(\Rightarrow 3^{936}\times 3^6\equiv 3^{942}\equiv 729 \mod 2014\)

Log in to reply

I want to ask How to read it or interpret this like when we do 12/3=4 , we say when 12 is divided by 3 we get 4 as a quotient.How to read it?

Log in to reply

\(12\equiv 1 \mod 11\)

is read as "12 congruent to 1 mod 11" or "12 equivalent to 1 mod 11"

Log in to reply

I always use Euler's totient function since it reduces exponents into a fathomable number. (Though I still do not know the proof of the theorem, would be great if someone presents one)

Log in to reply

U may find it here

Log in to reply

please explain it or give another way please please.........

Log in to reply

Sorry for my mistake I've now edited it. There's no other method to my knowledge. U can look up this theorem in the brilliant wiki.

Log in to reply

Log in to reply

@GAUTAM SHARMA Check out Euler's Theorem in the Modular Arithmetic Wiki. That should provide you with explanations about how to approach problems like this.

Log in to reply

Log in to reply