If n = (33)^43 + (53)^33 what is the units digit of n?	Choose the correct choice from the following
A) 0 B) 2 C) 4 D) 6 E) 8
First of all, the units digit of (33)^53 is the same as that of 3^53 and the units digit of (53)^33 is the same as that of 3^33. So, we need to find the units digit of 3^53 + 3^33.   Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:   3^1=3 (the units digit is 3)   3^2=9 (the units digit is 9)   3^3=27 (the units digit is 7)   3^4=81 (the units digit is 1)   3^5=243 (the units digit is 3 again!)   ...   Thus:   The units digit of 3^53 is the same as the units digit of 3^3, so 7 (53 divided by the cyclicity of 4 gives the remainder of 3).   The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).   Therefore the units digit of (33)^53 + (53)^33 is 7 + 7 = 4.   Answer: 4.
<result>C</result>
If n = (33)^43 + (53)^33 what is the units digit of n?