Question

Show that 15^n cannot end with 0,2,4,6,8 for any natural no.

Answer 1

Step-by-step explanation:

Let n = 1.

15^1 = 15, which ends with a 5.

Suppose the hypothesis is true for n and consider n + 1.

15^(n + 1) = 15^n * 15 = p * 15 for some integer p that ends with a 5.

Since the factors, p and 15, both end with a 5, their product, p * 15, will end with a 5.

Therefore, 15^(n + 1) ends with a 5.

Therefore, by induction, 15^(n + 1) ends with a 5 for all natural numbers, n.

Therefore, 15^n can not end with the digit 0.