Examine whether (24)ⁿ can end with the digit 5 for any n ϵ N.

If (24)ⁿ end with the digit 5, then the number should be divisible by 5.

This means the prime factorization of 24ⁿ should contain prime factors 5.

But (24)ⁿ = (2³ × 3)ⁿ and it does not have the prime factor 5 but have 3 and 2.

, 5 is not present in the prime factorization, there is no natural number nor which 24ⁿ ends with digit 5.

So, 24ⁿ cannot end with digit 5.