2017Regional Rajshahi Secondary

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samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm
2017Regional Rajshahi Secondary

Unread post by samiul_samin » Tue Feb 20, 2018 7:09 pm

What will be the remainder when $2016 ^{2016}$ is divided by $2017$?

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: 2017Regional Rajshahi Secondary

Unread post by samiul_samin » Tue Feb 20, 2018 8:00 pm

Hint
Use $\phi function$
Answer
$\fbox 1$
Solution
$2017$ is a prime.
So,$\phi(2017)=2016$
So,$2016^{\phi (2017)} \equiv 1 $mod$ (2017)$
$\Rightarrow 2016^{2016} \equiv 1 $mod$ (2017)$
The answer is $\fbox 1$

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