Hard one

[ladyp]

ok, I am still not sure how you guys solve this one. Can someone please explain it again. thx

this is what I understand...
x^n-1 therefore, x ^ 6 - 1 = x^5

[arjmen]

With some graft, An can be written in the form: x^(n-1) [1+x(1+x(1+x(1+x)))]

Dividing An by "x [1+x(1+x(1+x(1+x)))]" gives "x^(n-1)/x" since the terms in the box bracket cancel.

so we have,

x^(n-1)/x = x^5

=> x^(n-1) = x^6

Therefore, n=7