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?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 10
(A) 2
(B) 4
(C) 5
(D) 6
(E) 10
I got 4.
Not sure if it is right but here is my explanation:
if n^4 is divisible by 32, the n^4 must have at least five 2's in it's product.
since n^4 = n^2* n^2
every prime number in n must occur in sets of 2.
2*2*2*2*2 = 32;
32 is 2^5, so three more 2's need to be added to make n have four sets of two 2's.
so the smallest value n could possibly be is 4
4/32, would give the remainder of 4.
I am not sure if I explained it really well. What is the OA?
