The correct option is (a) 8
Best explanation: P(n) = 2^4n – 1
P(1) = 2^3 = 8
Let us assume P(k) is divisible by 8 and can be written as 8c, where c is any integer.
P(k) = 2^4k – 1 = 8c
P(k + 1) = 2^4(k + 1) – 1
P(k + 1) = 2^4k + 3
P(k + 1) = 2^4 . 2^4k – 1
P(k + 1) = 2^4 . 8c
Clearly, P(k + 1) is divisible by 2, 4, 8 and 16.