Find a counterexample to the statement 4^n + 1 is divisible by 5.

What about n=-2? or n=0? or n=2?

They are looking for just 1 right? how would I go about showng my work?

never mind I got it

To find a counterexample for the statement "4^n + 1 is divisible by 5," we need to find a value of n for which 4^n + 1 is not divisible by 5.

Let's try a few values of n and see if we can find a counterexample:

For n = 0:
4^0 + 1 = 1
1 is not divisible by 5, so this is a potential counterexample.

For n = 1:
4^1 + 1 = 4 + 1 = 5
5 is divisible by 5, so this is not a counterexample.

For n = 2:
4^2 + 1 = 16 + 1 = 17
17 is not divisible by 5, so this is another potential counterexample.

By continuing this process, we can find more counterexamples.

Therefore, we have found counterexamples to the statement "4^n + 1 is divisible by 5" for n = 0 and n = 2, among others.