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.

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