prove by induction that 4^n-1 is divisible by three for all posotive integers of n

any help would be appriciated thanks.

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- January 28th 2009, 07:38 AMhmmmmproof by induction
prove by induction that 4^n-1 is divisible by three for all posotive integers of n

any help would be appriciated thanks. - January 28th 2009, 07:51 AMrunning-gag
Hi

Initialization of induction is easy.

Let's suppose that for a given n is divisible by 3.

You need to demonstrate that is divisible by 3.

Hint : . - January 28th 2009, 08:01 AMskeeter
prove is divisible by 3

true for

assume true for , show true for ...

since is divisible by 3, then , a positive integer.

since is also a positive integer, is a multiple of 3, and therefore, is divisible by 3. - January 28th 2009, 08:11 AMSoroban
Hello, hmmmm!

Here's another way . . .

Quote:

Prove by induction that for all positive integers

Verify . . . true

Assume

Add to both sides: .

Factor: .

. . . . . . . .

. . . . . . . .

We have proved . . . The inductive proof is complete.