Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
$25^{25}$ is divided by 26, the remainder is
(a)1
(b)2
(c)24
(d)25
Answer
Answer (as printed): D
Explanation
$\left(x^{n}+a^{n}\right)$ is divisible by $(x+a)$ when $n$ is odd. $$\begin{aligned} & \therefore\left(25^{25}+1^{25}\right) \text { is divisible by }(25+1) \\ & \Rightarrow\left(25^{25}+1\right) \text { is divisible by } 26 \end{aligned}$$ ⇒ On dividing $25^{25}$ by 26, we get $(26-1)=25$ as remainder.
Explanation as extracted from the printed page; notation may be imperfect.