Q1: What will be remainder when 17²⁰⁰ is divided by 18 ?

ANS:C - 1

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.