Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
If $7^{126}$ is divided by 48, find the remainder.
Answer
Answer (as printed):
Explanation
$7^{126}=(7^{2})^{63}=(49)^{63}$. Now, since $(x^{n}-a^{n})$ is divisible by $(x-a)$ for all values of $n$, so $[(49)^{63}-1]$ or $(7^{126}-1)$ is divisible by $(49-1)$ i.e. 48. Remainder obtained when $7^{126}$ is divided by 48 = 1.
Explanation as extracted from the printed page; notation may be imperfect.