Tuesday, 5 June 2018

elementary number theory - An easy way to calculate $12^{101} bmod 551$?

We learn about encryption methods, and in one of the exercises we need to calculate: $12^{101} \bmod 551$.




There an easy way to calculate it?
We know that: $M^5=12 \mod 551$
And $M^{505}=M$ ($M\in \mathbb{Z}_{551}$).



(Our goal is to find $M$).
I try to use Fermat, Euler but they can't help me here, right?



P.S. - The idea is to calculate it without calculator...



Thank you!

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