Question

Find integer x such that \(1 10 years ago

Answer 1

bonus question: :) how to find the factors of 32767 without trial and error? I meant test one by one?

Answer 2

32767 = 7 × 4681, so 232767 − 1 is a difference of seventh powers. You can factor a difference of seventh powers in a similar way to how you factor a difference of cubes

Answer 3

for some reason 32767 is familiar to me because\[32767 = 2^{15}-1\]

Answer 4

32767 = 31*1075
= 151*217

Answer 5

So that we can see many factors of 32767, how can we know which one we will use to find x?

Answer 6

well you wrote 232767 − 1 as a difference of 4681st powers there instead of a difference of seventh powers as I suggested, but you can do it that way too if you really want to.
Where a = 27 and b = 1 (27 -1){(27 )2 +27 *1+ 12}
No, you are using the difference-of-cubes factoring formula there, which says a3 − b3 = (a − b)(a2 + ab − b2). But what you have is not a difference of cubes! You have written a difference of 4681st powers, not a difference of cubes. If you take a = 27 and b = 1, then what you have is a4681 − b4681, not a3 − b3, so it does not factor as (a − b)(a2 + ab − b2), because that's the factorization of a3 − b3, not a4681 − b4681.

Answer 7

so see if 2^32767 is divisible by 2

Answer 8

@imqwerty binomial theorem? :P

Answer 9

N=32767=7*31*151
Hint :
(2^n-1)/(2^d-1) is integer s.t d|n

Answer 10

@ikram002p which theorem are you using?

Answer 11

m not going with binomial directly rn
trynna reduce the terms

Answer 12

@ikram002p nvm, I got it.

Answer 13

Thanks all. I got how to find it out. :)

Answer 14

is the answer 3?

Answer 15

no

Answer 16

aww just a min ima check again
nd yeah i culdn' get a better form
binomial wrked

Answer 17

:O

Answer 18

hey are you there?