Question

check whether (15)n can end with the digit 0 for any neN

Answer 1

15^n is a natural number. If we look at its prime factorisation, we get (3*5)^n.

Now, we already know that for a number to end with 0, its prime factorisation must be written in the form of 2^n and 5^n. Since 2 is not in the prime factorisation of 15^n. It can not end with the digit 0.

(Also, The uniqueness property of Fundamental theorem of Arithmetic guarantees us that there is no other prime factorisation but this.)

Hope it helps!