Find the remainder when 3^100 is divided by 7 using modulus. Answer is 4 but I can't under stand how is it

Question

anonymous · Answer

look for the patter, although there might be a fancier way to do it

anonymous · Answer

*pattern

anonymous · Answer

$3^1$ remainder is 3
$3^2$ remainder is 2
$3^3$ remainder is 6
$3^4$ remainder is 4

when you get to 1 it will start over

parthkohli · Answer

A fancier way to do it is$$3^{n} \equiv 3^{n - 5} \times 3^5 \equiv 3^{n-5} \pmod{7}$$You can look smart with this trick by just looking at the pattern lol

loser66 · Answer

got it? need more explanation?

loser66 · Answer

when I studied this stuff, I was struggling to understand , hiihi,,, know how you feel