If n is an integer and n^4 is divisible by 32, which of the following could be the remainder when n is divided by 32?
Answers:
A) 2
B) 4
C) 5
D) 6
E) 10
Given:   n^4/32 = int   n^4/2^5 = int   1/2(n/2)^4 = int   try n= int = 2,4,6,8... because n/2 must be an integer   n=2 wont work because 1/2(n/2)^4 needs to be an integer.   n=4, result = 1/2 (2)^4 = 8, so the remainder of n/32 = remainder of 8/32 = 8 (not an option)   n=8, result = 1/2(8/2)^4 = 1/2(4)^4 = 1/2x16x16= 16x8, so the remainder of n/32 = remainder of 16x8/32 = 4 (option 4)
<result>B</result>
If n is an integer and n^4 is divisible by 32, which of the following could be the remainder when n is divided by 32?