Show that 5 n can't end with the digit 2 for any natural numbers.

The number 5n for any value of n to end by 2, 5 n should be divisible by 2.

As to end with the number 2, we also should have 5ⁿ divisible by 2. But this is not at all possible as 5ⁿ contains only 5 and 1. So by the uniqueness theorem of arithmetic, there is no other factor of 5ⁿ other than the 5 and 1 here.

Therefore, 5ⁿ cannot end with the digit 2 for any natural number n.