Question

Find a counterexample to the statement 4^n + 1 is divisible by 5...how do i show my work for this problem? The example in my book is too confusing it doesnt really go into detail but just shows a table.

Answer 1

What happens if yo put n = 1?

Answer 2

I get 4^1+1=5 divided by 5 =1?

Answer 3

NVM i figured it out =)

Answer 4

n=2

Answer 5

4 = -1 [5]
4^n = (-1)^n [5]
4^n + 1 = (-1)^n + 1 [5]

so if n=2k+1 4^n + 1 is divisible by 5