k = 2^n + 8, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?
Answers:
A) 2^n - 8  B) 2^n - 2  C) 2^n  D) 2^n + 4  E) 2^n + 5
Given: k, M and N are integers   If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N)   We're told that 9 is a divisor of 2^n + 8   We also know that 9 is a divisor of9.   So, applying the above rule, 9 is a divisor of 2^n + 8 +9, and 9 is a divisor of 2^n + 8 -9=2^n -1   2^n + 4
<result>D</result>
k = 2^n + 8, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?