If n = (33)^40 + (43)^33 what is the units digit of n?	Answers:	A) 1	B) 2	C) 4	D) 6	E) 8
First of all, the units digit of (33)^40 is the same as that of 3^43 and the units digit of (40)^33 is the same as that of 3^33. So, we need to find the units digit of 3^40 + 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 3^40 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3).   The units digit of 3^30 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)^40 + (40)^33 is 7 + 4 =1.   1nswer: 1.
<result>A</result>
If n = (33)^40 + (43)^33 what is the units digit of n?