Question

$8^{4n}-7^{4n}$ is divisible by which of the following?

• A. 15
• B. 113
• C. 23
• D. more than one of these

Answer 1

The correct option is D

more than one of these

$(8^2{)}^{2n}-(7^2{)}^{2n}$ is of the form $a^n-b^n$ where the power is always even because 2n is always even.

That means it is divisible by $8^2+7^2$ as well as $8^2-7^2$.

Check for n=1, it becomes $8^4-7^4$, which is divisible by $8^2+7^2$ and $8^2-7^2$.

Thus. the given number is divisible by both 15 and 113.