using binomial therorem, 32n+2-8n-9 is divisible by 64, n belongs to N
In order to show that 32n+2 - 8n - 9 is divisible by 64, it has to be proved that,
, where k is some natural number and
32n+2 = 32.(n+1) = 9n+1 ..... (1)
By Binomial Theorem,
For a = 8 and m = n + 1, we obtain
⇒ 32n+2 - 8n - 9 = 64k [using (1)]
Thus, 32n+2 - 8n - 9 is divisible by 64, whenever n is a positive integer.