Problem Solving

Hey,

can anyone answer this question:

If n is a positive integer, what is the remainder when 3^4n+2 + 1 is divided by 10?

I'm really struggling with this one. I would appreciate any help on this. Thanks

...there is no remainder, or am i mistaken?

is this 3^(4n + 2 + 1) or 3^(4n) + 2 + 1

FinanceBioE: To clarify, the question is:

3^(4n + 2) + 1 divided by 10.

Svedankae, you are correct. The answer is 0, there is no remainder. Could you please show me how you came to this answer?

Thank you very much.

3^(4n+2) can be written as 3^4n * 3^2 = 9 * 3^4n.

For all n = 0, 1, 2, 3 ..., the units digit of 3^4n is 1.

n=0; 3^0 -> units digit is 1
n=1; 3^4 -> units digit is 1
n=2; 3^8 -> units digit is 1
...

=> the units digit of 9 * 3^4n is 9, to which when 1 is added the units digits would be 0, which is clearly divisible by 10 and hence the remainder is 0.

Thank you ichip_tpt. This explanation is perfect.