If the units digit of n^31 is 7, which of the following could be the value of n?
I. n = 41
II. n = 43
III. n = 47	Select:
A) Only I
B) Only II
C) Only III
D) I and II
E) II and III
I tried in this way.   Given n^31 units digit is 7.   If at all we have to get 7 as units digits only 3 and 7 series has 7   3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81   7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units)   We have n^31 - then divide 31 by 4 = reminder 3.   Then we have for only 7^3 - we have units digit as 3.   Hence 47^31 = 7 (units).   Option Only II is correct answer , and with 41^31 we always get 1 as units digit and 43^31 - we get units as 3.
<result>B</result>
If the units digit of n^31 is 7, which of the following could be the value of n?
I. n = 41
II. n = 43
III. n = 47