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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 4 years, 1 month ago

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\(\phi(2014)=936\)

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

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

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

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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);.

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## Comments

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

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

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

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

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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?

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\(12\equiv 1 \mod 11\)

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

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

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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.

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@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.

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