Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
If $\left(67^{67}+67\right)$ is divided by 68 , the remainder is
(a)1
(b)63
(c)66
(d)67
Answer
Answer (as printed): C
Explanation
$\left(x^{n}+a^{n}\right)$ is divisible by $(x+a)$ when $n$ is odd. $$\begin{aligned} & \therefore\left(67^{67}+1^{67}\right) \text { is divisible by }(67+1) \\ & \Rightarrow\left(67^{67}+1\right) \text { is divisible by } 68 \end{aligned}$$ ⇒ On dividing $\left(67^{67}+67\right)$ by 68, we get $(67-1)=66$ as remainder.
Explanation as extracted from the printed page; notation may be imperfect.