JEE Main 2016 (18)

Number Theory Level 4

Find the remainder when $2222^{5555}$ is divided by 7.

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5 1 2 0 4 6 3

1 solution

Akshat Sharda
Mar 21, 2016

$2222^{5555}\equiv 3^{5555} \pmod 7 \\ 3^{\phi(7)}=3^6\equiv 1\pmod 7 \\ 3^{5555}\equiv 3^{5}\equiv \boxed{5} \pmod 7$

This variety of question is sure to not to be asked in JEE-Main. What do you think?? (+1)

Rishabh Jain - 5 years, 2 months ago

No , but it's under $binomial theoram$ .

$\eta$ = $2222^{5555}$ = $(317\times 7 + 3)^{5555}$ .

Let us define $R_n(.)$ as remainder when $(.)$ by $n$ .

$R_7(\eta)$ = $3^{5555}$ = $243^{1111}$ = $5\times 5^{1110}$ = $5\times (-1)^{370}$ = $\boxed{5}$

Aakash Khandelwal - 5 years, 2 months ago

I also believe that question level in this set is much higher than mains level. Many questions have more than 4 options while in jee mains, all the questions have 4 options.

Akhil Bansal - 5 years, 2 months ago

I also feel the same that's why I would not be attempting this set any more.. Questions are good but are irrelevant for JEE mains..

Rishabh Jain - 5 years, 2 months ago

@Rishabh Jain – Come on slack! Exams over?

Akshat Sharda - 5 years, 2 months ago

@Akshat Sharda – He has JEE...

A Former Brilliant Member - 5 years, 2 months ago

@A Former Brilliant Member – Oh! I just forgot about it!

Akshat Sharda - 5 years, 2 months ago

@Akshat Sharda – Yeah.. Surely I'll join after JEE ADV in June... :-)

Rishabh Jain - 5 years, 2 months ago

@Rishabh Jain – soo, what rank did you get in jee adv 2016 ?

A Former Brilliant Member - 4 years, 10 months ago

Yeah NT is not there for JEE I think isnt it ?

A Former Brilliant Member - 5 years, 2 months ago

Exactly.. JEE Main questions are straightforward formula putting( with few exceptions)... And NT is not in syllabus.. Even in ADVANCE NT is not in syllabus..

Rishabh Jain - 5 years, 2 months ago

@Rishabh Jain – Yeah they are in Olympiad syllabus but I being in 10th solve all types of questions.

Kushagra Sahni - 5 years, 2 months ago

@Rishabh Jain – I think you are right!

Akshat Sharda - 5 years, 2 months ago

@Rishabh Jain – So hows your preparation going :) ?

A Former Brilliant Member - 5 years, 2 months ago

@A Former Brilliant Member – Good.. :-)

Rishabh Jain - 5 years, 2 months ago

BTW, this question is in the example section of arihant publication book used for jee (author:- S.K Goyal)..

Ankit Nigam - 5 years, 2 months ago

What is $\phi$ here

Navin Murarka - 3 years, 2 months ago

JEE Main 2016 (18)

Try my set: JEE main 2016 .

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