Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
When $2^{256}$ is divided by 17, the remainder would be
(a)1
(b)14
(c)16
(d)None of these
Answer
Answer (as printed): A
Explanation
When $n$ is even, $\left(x^{n}-a^{n}\right)$ is divisible by $(x+a)$. Now, $2^{256}=\left(2^{4}\right)^{64}=(16)^{64}$. $\therefore\left(16^{64}-1^{64}\right)$ is divisible by $(16+1)$ $\Rightarrow\left(16^{64}-1\right)$ is divisible by 17 $\Rightarrow\left(2^{256}-1\right)$ is divisible by 17 ⇒ On dividing $2^{256}$ by 17, we get 1 as remainder.
Explanation as extracted from the printed page; notation may be imperfect.