Question

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

Answer 1

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

Answer 2

*pattern

Answer 3

\(3^1\) 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

Answer 4

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

Answer 5

got it? need more explanation?

Answer 6

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