When n is even. (xⁿ - aⁿ) is completely divisibly by (x + a)

(17²⁰⁰ - 1²⁰⁰) is completely divisible by (17 + 1), i.e., 18.

    (17²⁰⁰ - 1) is completely divisible by 18.

    On dividing 17²⁰⁰ by 18, we get 1 as remainder.