mathematical induction problem

Use mathematical induction to prove the following:
a factor of (9^n - 8n - 1) is 64 for all n > or = 2

9^1 - 8 - 1 = 64a
64 = 64a

where a = any integer

9^k - 8k - 1 = 64a

prove that 9^(k+1) - 8(k+1) - 1 = 64b; where b = any integer
9(9^k) - 8k - 9

so that's how far i've gotten and now i'm stuck. please help me.

First show that the statement is true for n = 2. Which infact is.

Now assume

is true.

Consider



Which is same as


which on simplification gives

Now by assumption is divisible by 64 and for k > 2 64k is divisible by 64.
So statement is true for k + 1

Hence proved.

P.S I am new to this forum and am learning how to type mathematical expressions. So ignore any typing mistake.

Quote:

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Originally Posted by oblixps

Use mathematical induction to prove the following:
a factor of (9^n - 8n - 1) is 64 for all n > or = 2

9^1 - 8 - 1 = 64a
64 = 64a

where a = any integer

9^k - 8k - 1 = 64a

prove that 9^(k+1) - 8(k+1) - 1 = 64b; where b = any integer

9(9^k) - 8k - 9

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Thanks skeeter. That was very clear way to explain. I went bit gross in my explanation. :)

thank you very much for the help guys! (Nod)