Euler's theorem 3

Number Theory Level 3

Find the remainder when $29^{202}$ is divided by 13.

The answer is 3.

1 solution

Ayush G Rai
May 25, 2016

easy peasy again

@Ayush Rai @abhishek alva Please be respectful of the community and supportive in your comments. We do not approve of insulting taunts. Repeat offences will result in the deactivation of your account.

Calvin Lin Staff - 5 years ago

Actually abhishek is my cousin and we are used to insulting at each other.btw I had told him to join slack.I'm sorry.

Ayush G Rai - 5 years ago

write the solution.

(Edited by Calvin)

abhishek alva - 5 years ago

there is a pattern for this question.
when $29^1$ is divided by $13$ the remainder is $3.$
when $29^2$ is divided by $13$ the remainder is $9.$
when $29^3$ divided by $13$ the remainder is $1.$
when $29^4$ divided by $13$ the remainder is $3.$
when $29^5$ divided by $13$ the remainder is $9.$
when $29^6$ divided by $13$ the remainder is $1.$
The pattern goes on like $3,9,1,3,9,1\dots$
So there are only three options 3,9,1.then the answer must be one of them that is $\boxed 3.$

(Edited by Calvin)

Ayush G Rai - 5 years ago

try euler's theorem 1 and 4.

(Edited by Calvin)

abhishek alva - 5 years ago

@Abhishek Alva – I had already got 1,2,3 but not 4.join slack.check your email.try out my problems.they are way harder than yours.

(Edited by Calvin)

Ayush G Rai - 5 years ago

Euler's theorem 3

The answer is 3.

1 solution

0 pending reports