Sweet 17

Number Theory Level 3

Let $x$ be any positive integer greater than $17^{17}$ , which is not divisible by $17$ .

Then which of the following is always true :

A: either $x^8-1$ , or $x^8+1$ , is divisible by $17$ .

B: either $x^9-1$ , or $x^9+1$ , is divisible by $17$ .

C: either $x^8-1$ , or $x^9+1$ , is divisible by $17$ .

D: either $x^8+1$ , or $x^9-1$ , is divisible by $17$ .