Question

For every natural number n > 1, show
that
\[
n^6 - n
\]
is divisible by 56786730
Notice that
\[
56786730=2\times 3\times 5\times 7\times 11\times 13\times
31\times 61
\]

Answer 1

how is 2^6-2 divisible by that mammoth no. btw? I don't see how..

Answer 2

or maybe I am unable to comprehend what the question means.

Answer 3

\[
\frac{2^{61}-2}{56786730}=4060
5314115
\]
Sorry,
I have a misprint
\[
n^6 -n
\]

Answer 4

Ohkay, np. now let's think.

Answer 5

is it 61??

Answer 6

Yes,
I closed this question and posted the corrected one.

Answer 7

It is
\[
n^{61} -n
\]