Problem Solving

If n is a positive integer, what is the remainder when 3^(8n+3) + 2 is divided by 5?

a. 0
b. 1
c. 2
d. 3
e. 4

OA = E

I understood that the key to the problem was to discover the pattern of powers of three, with respect to the units digit:
3^1 = 3
3^2 = 9
3^3 = 7 (27)
3^4 = 1 (81)
3^5 = 3 (243)

but after this point, I lost my way. Can someone please walk me through. Thanks

Whenever there is a rule in the question, we can pick a number that satisfies that rule....n is a positive integer. Let it be 1.

Then, we have 3^11 plus 2. We know that the units digit of successive powers of 3 follow the cycle of 4 you outlined above (other numbers follow other cycles for thier units digit; but they all follow a cycle). So, the units digit of 3^11 is 7. But when we add the 2, the units digit becomes 9. And 9 divided by 5 leaves a remainder of 4.