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"What is the remainder of $3^{12194}$ when divided by 17?"

So I'm trying to work this out using Fermat’s Little Theorem which I know we can use for a fact because 17 is prime with GCD(3,17)=1 and I've tried using it and other questionable methods to at least calculate the remainder of $3^{12194}$ before doing the division part but I just keep getting incorrect answers and quite frankly I have no idea as to why. Would appreciate it if someone could show how this is supposed to be done correctly.

Arturo Magidin
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    “FLT” is usually understood (in the number theory context) to stand for Fermat’s Last Theorem; what you want here is probably the so-called “Fermat’s Little Theorem”, which is never abbreviated “FLT”. (And in other contexts, ‘flt’ may stand for “Faster than Light Travel”). – Arturo Magidin Feb 15 '21 at 21:44
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    You mean $3^{16}\equiv 1\pmod{17}$, then $12194=16\times762+2$ hence $3^{12194}\equiv{3^{16}}^{762}\cdot3^2\equiv 9\pmod{17}$? – Jean-Claude Arbaut Feb 15 '21 at 21:45
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    There are several duplicates to this popular question. This post explains it in general, other ones give some more examples to use little Fermat and other methods. – Dietrich Burde Feb 15 '21 at 21:46

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