Question

Which of the following numbers will completely divide $({49}^{15}-1)$?

• A. $8$
• B. $14$
• C. $46$
• D. $50$

Answer 1

Answer: (A)

$8$

$(x^n-1)$ will be divisible by $(x+1)$ only when $n$ is even.
$({49}^{15}-1)=\{{\left(7^2\right)}^{15}-1\}=(7^{30}-1)$, which is divisible by $(7+1)$ i.e., $8$.