For any natural number n the expression 9²n − 4²n is divisible by

The expression 9²n − 4²n can be written as (81ⁿ − 16ⁿ). This is always divisible by both 5 and 13 due to properties of modular arithmetic. When powers are raised to natural numbers the differences maintain divisibility by these constants. This shows how number theory can be applied to exam questions. It is an example of modular congruence used in advanced mathematics.