for all n>=3 prove that 2^{n+1}does not divide 3^{^2^(n-2)}- 1

i have figured out by crunching numbers that 2^{n}divides 3^{^2^(n-2)}- 1 but having trouble trying to start a proof. any help appreciated.

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- February 21st 2013, 09:11 AMwingtipneed help disproving
for all n>=3 prove that 2

^{n+1}does not divide 3^{^2^(n-2)}- 1

i have figured out by crunching numbers that 2^{n}divides 3^{^2^(n-2)}- 1 but having trouble trying to start a proof. any help appreciated. - February 21st 2013, 09:25 AMMagnechuRe: need help disproving
- February 21st 2013, 09:48 AMwingtipRe: need help disproving
so prove it does not work for n=3, then show it does not work for n=4? i feel as though there should be a more solid proof than that.

- February 27th 2013, 02:58 PMMagnechuRe: need help disproving
It's a general inductive proof. You show for n=3, assume for n-1, and show it holds for n.