Question

Check if \(2^{12} - 1\) is divisible by 13.

Can I use Fermat's Little Theorem here?

Answer 1

I get yes as the answer.
\(2^{13 - 1} - 1 \) if you rephrase it.

Back to the definition of the theorem:
\(a^{p - 1} - 1\) is divisible by \(p\).

Am I right?

Answer 2

Here, \(p = 13\).

Answer 3

three one five?

Answer 4

?

Answer 5

he means \(315\) as the answer

Answer 6

I just wanted to check if it was divisible.

Answer 7

Oh yes, then it is divisible!

Answer 8

yeah; you can use induction as well i think

Answer 9

Why use induction? There is no \(k\) or \(n\) or \(x\) here.

Answer 10

Well so I was correct, wasn't I?

Answer 11

i know lol change the 12 into n

you are correct anyway but dont trust me

Answer 12

Well, now as I have an integer quotient, I must be correct.

Answer 13

yeah lol.
no medal is needed for me; i didnt do anything