9ⁿ - 1 is divisible by 8 for all non-negative integers. Please solve the Theorem .... unable to find the solution on the net.?

let P(x) = x^n-1

It is always divisible by x-1

this can be proved using the factor theorem.

P(x) = x^n-1 is divided by x -1

P(1) = 1^n-1 = 0

Using this theorem we shall answer your question :

8 can be written as 9 - 1

consider 9 as "x" in this case and proceed.

then the question becomes same as the theorem proved above !!

Hope this helps