Question

If n is a natural number, then 9²ⁿ − 4²ⁿ is always divisible by ______.

Options

•  5

• 13

• both 5 and 13

• None of these

Answer 1

If n is a natural number, then 9²ⁿ − 4²ⁿ is always divisible by both 5 and 13.

Explanation:

Given, 9²ⁿ − 4²ⁿ is in the form of a²ⁿ − b²ⁿ where n is a natural number.

Since a²ⁿ − b²ⁿ is always divisible by (a − b) and (a + b),

9²ⁿ − 4²ⁿ is always divisible by:

9 − 4 = 5

9 + 4 = 13

∴ 9²ⁿ − 4²ⁿ is always divisible by both 5 and 13.