If n is a positive integer, what is the remainder when (7^(3n+3))(6^n) is divided by 10?	Choose the correct choice from the following choices:
A) 1
B) 2
C) 4
D) 6
E) 8
This one took me bout 3 1/2 min. Just testin numbers and what not.   First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p.   1-7 stands for ^1 thru 7   1: 7*1=7   2: 7*7=9   3: 7*9=3   4: 7*3=1   5: 7*1=7   6: 7*7=9   7: 7*9=3   Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems.   so 7^4n+3 ---&gt; if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--&gt; 18/10 --&gt; R=8   Now from here if id double check just to make sure.   7^4(2)+3*6= 
<gadget id="calculator">3*6</gadget>
<output>18</output>
18/10 ---&gt; R=6.   6 or J in this problem.
<result>D</result>
If n is a positive integer, what is the remainder when (7^(3n+3))(6^n) is divided by 10?