If n is a natural number then 9²n − 4²n is divisible by

For any natural number n the expression 9²n − 4²n can be written as (81ⁿ − 16ⁿ). By using modular arithmetic we can show that this is divisible by both 5 and 13. It is a property of numbers where differences of certain powers give factors. This result is consistent for all natural numbers n.