Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
If $17^{200}$ is divided by 18, the remainder is
(a)1
(b)2
(c)16
(d)17
Answer
Answer (as printed): A
Explanation
When $n$ is even, $(x^{n}-a^{n})$ is divisible by $(x+a)$. $\therefore (17^{200}-1^{200})$ is divisible by $(17+1)$ $\Rightarrow (17^{200}-1)$ is divisible by 18 $\Rightarrow$ On dividing $17^{200}$ by 18, we get 1 as remainder.
Explanation as extracted from the printed page; notation may be imperfect.