Suppose n a a Prove that n4 is divisible by 3 iff n is divi

Suppose n . a)

a) Prove that n4 is divisible by 3 iff n is divisible by 3.

b) Show that it is false that n2 is divisible by 12 iff n is divisible by 12.

Pls write clearly & explain each step. ty.

Solution

a)

Let n^4 be divisible by 3

But 3 is a prime hence, 3|n

Now let n be divisible by 3

So, n=3k for some integer k

So, n^4=3^4k

hence n^4 is divisible by 3

b)

We will show using a counterexample

Let, n=6

n^2=36 is divisible by 12 but n=6 is not